Assuming, as you've requested, that "that's boring, don't track it" is off the table, then yes, your intuition is right: this is a logistics problem. And to the contrary, it is the bread and butter of many groups' style of playing D&D, with a tradition stretching back to the very first days of the hobby in the early 1970s. Liking these ideas and wanting to involve them in your roleplaying is not in vogue now, but it is certainly within the range of acceptable ways of playing D&D. (I personally quite like the challenges and "putting myself into their head" feel of playing in this way.)
And, wonderfully, D&D 5e is flexibly designed in such a way that it can easily be played in this way without fighting the game.
If it being a logistics problem is valid for a group's approach to the game, then it's one of the fundamental puzzles that the players are responsible for solving, and doing so requires accounting for where everything goes, both in the sense of "accounting" as keeping track of things, and in the sense of justifying themselves.
When you're playing the game like this, you appeal to real-world knowledge, except insofar as the game provides replacement rules or guidelines that replace your real-world knowledge. (All RPG rules work like this — replacing or modifying your default knowledge of how things work — but that's especially true for managing mundane issues like this.)
So, with that preamble out of the way, where does all that stuff go?
Accounting for your stuff
A backpack only holds so much, yes. As you can in real life though, you can strap stuff to the outside, hang stuff off the bottom, and carry things in your hands while walking. That absurd hunting trap can go anywhere you can justify, and there are as many ways to solve the question of "where do I pack this?" as there are people with different gear-packing strategies. I'd hang it off the bottom of the pack, myself, but maybe you have other things that would better go there? Just like packing for a real hiking trip, things get juggled around until it all just works — or you give up on an item as too much bother to take with you.
Once you figure out a place for everything and everything's in its place, you've solved the problem of "how" naturalistically.
Swords, shields, ammo, and clothes
Indeed, items of combat equipment don't go in a backpack. Or they could, I guess, but that's an inconvenient place for them. Scabbards let you carry a sword on your belt with ease, and also make it quick to wield. A quiver does the same for ammo. These free up your backpack and hands for other gear. Shields get strapped to whatever they can be solidly strapped to, such as over the backpack or hung off the saddle.
Quivers (for arrows) and cases (for crossbow bolts) are listed in the equipment tables with prices and weights, so they don't come with the ammo and you have to buy one, and they aren't weightless. (A note to the less logistics-minded readers: without "a quiver, case, or other container" for your ammo, you don't get the benefit of the Ammunition weapon property's free reloading rules.)
Scabbards are not listed in the equipment chapter. Since swords on the smaller side are fairly useless without somewhere to keep them, it's probably safe to assume they come with scabbards when you buy them. (I personally find this a curious oversight, especially since quivers and cases are detailed, and other editions with "you want logistics? you can do logistics" levels of equipment detail do list scabbards. You may wish to add an entry for scabbards to the equipment lists your group uses. After all, when you find a bare blade in a dragon's hoard, you're going to want to buy a nice scabbard for it, right?)
Most armour, including plate harness, was worn over some kind of clothing. You might want a spare change in your pack, or you can just be grubby between the baths and laundry service provided at the inns you stop at. Medieval-level societies were often pretty filthy by default, so your character has a range of legitimate/believable choices in the realm of hygiene.
Sharing the burden
And speaking of saddles, when you've got too much gear to conveniently carry, that's where a pack horse, donkey, or riding horse comes in. (People who can't afford a beast to carry their stuff would dump it in a hand-cart instead — and though that's not a great way to travel long distances with all your possessions, people did what they had to, and sometimes travelling a long way with all your possessions in a hand cart is what people had to do. Hopefully your adventurer is more financially successful by the time they have to haul more than they can personally carry, though, and won't be reduced to such a sorry state.)
Carrying the loot
If you're well-equipped, you're probably already pretty burdened just with "necessary" gear. That doesn't leave much room for extra stuff you find in your travels, like piles of gold that can buy you that mule back in town. Old-school D&D players have long since figured out the solution to this: the sack. Sacks are lightweight, small to pack when empty, can carry literal sacks of gold, and can be carried one in each hand while travelling, leaving your packed pack unmolested by the storage needs of the new stuff. If only lightly filled, a sack can be tied to a belt, and carried even more easily.
The humble sack is a treasure-hunter's best friend, even ranking before the mule to carry even more sacks.
Less amazing than the sack, but still useful, is the belt pouch. Easily carried on the belt (or belts, if you opt to wear a second one over a shoulder, crossing your chest), pouches add a small amount of carrying space at no extra inconvenience for managing them.
Isn't this all unwieldy when actually, y'know, adventuring?
Yes, it is. Fighting while holding two sacks full of dragon's gold is not really going to end well. Or begin well, really. When combat looms, the traditional response (here, tradition referring to the grognardiest RPGers who have been playing this logistics-heavy way for decades and still are) is just as simple: drop your sacks and maybe even your pack to reduce your personal encumbrance, and then have at them with sword, bow, and spell.
Then, pray you don't have to run away — or if you do, you have a chance to snatch your treasure and gear back up!
A pack animal makes this easier yet: drop their lead when combat looms, and advance far enough forward that the melee doesn't come near the animal and spook them. (Though, tracking down a spooked animal with all your loot and gear on it can be an interesting adventure all its own, and lead you to places you might otherwise have never found!)
Better yet, hire a handler to hold your animal's lead while you, their master, engages the enemy in combat. Obviously you have to pay them, but the convenience of knowing your animal isn't going to run off unattended is worth paying for. Of course, that's assuming that they're loyal henchmen, but that's why you pay well, maintain a good reputation, get to know them at a personal level, and learn leadership skills that inspire people to be loyal followers rather than double-dealing traitors.
Plus, the risks and rewards of having and handling hirelings adds another social dimension to the game, which adds interest to play, and provides for another direction for complications and opportunities to arrive and convolve your gameplay. The more ingredients going into a roleplaying situation, the more engaging and emergent the situations that result. Just like a straying pack animal can lead to adventure, so can friendship and friction with a servant. But how the mundane can convolve play situations into deeply-engaging adventure is itself a whole other subject...
3k at level 8 is abysmally poor.
I can see why your PCs are clamouring for wealth, it's not vanity, Pathfinder is balanced around wealth being used for magic items for survival so they are going to be struggling to survive.
If they are point-buy-20 or higher they should have over 66'000gp by this point.
Things you are going to have to do to reduce the difficulty:
Limit high crit weapons
As you play the game longer and longer the chance of any player ever getting hit by a crit goes up to something like 80% (this is ever being hit, not any single chance). Also, critical damage can go up hugely as well. As you have been so stingy they cannot afford anything like a Buffering Cap you must never have weapons with 3x crit range and ideally no 19-20/2x crit range either. They aren't going to be able to take a critical hit and you have left them no opportunity to protect themselves.
Limit weapon damage
Because you haven't left wealth for things like Shawl of Life Keeping to give a buffer for general damage loss you need to dial things back a lot. If game guides would suggest enemies armed with greatsword (2d6), arm them with something like a Longsword (1d8) instead.
Makes things close yet environment to your PC's advantage
The utter lack of wealth of course is going to limit PCs ability to extend the range of their attacks, for example Rogue could never afford Assassin's Sight, so you're going to have to keep things a lot closer yet leave plenty of leeway for your players to disengage or use a height or cover advantage. They are going to need it.
Nerf enemies' stats
Your players should have been able to afford items to boost their core stats by now but obviously cannot. So knock a few points off enemy NPC strength and constitution. Or at least impose some limit like they've been fighting and are lower HP already or are suffering from a disease, tired from travelling, their weapons are damaged or are inherently intimidated by the PC's combat prowess (see sickened, fatigued, broken and shaken respectively).
Still, all is not lost, there's still a lot of very good cheap stuff out there that I can recommend that will be appreciated despite their low cost.
This very cheap item can be hugely appreciated should they be in fear of falling.
Ammunition can be enchanted in groups of 50, so individual units of ammunition would cost 1/50th of enchanting the lot. This can be a great way of cheaply handing out single use bonuses such as Bane Bolt/Arrow against a particular troubling enemy type.
Another cheap item of huge use IF you are a generous GM and give opportunity to use it such as flat roofs nearby that with contracting rope they could quickly get up onto.
Short of being able to boost their Constitution or have a magic item buffer their HP, this will have to do for the big fights. This allows them to stay conscious but staggered when they go to negative HP and Troll Oil stops the steady tick-tick loss of HP when reduced to sub-zero HP.
Very cheap item but gives a considerable buff to protect them from being grappled.
A cheap poison with a very useful effect in how since it requires two saves to end the effect it always works. If your PCs are worries about self poisoning then Blackfinger Paste can cover that concern.
Low CL Potions (50gp+)
There are many 1st level spells which are really good but hard to get out and are viable even at the absolute minimum caster level.
- Touch Of The Sea: can make up for inability to buff stats to be a good swimmer.
- Enlarge Person: is a 1 Round to cast but as little as a Standard action to imbibe
- Blend With Surroundings: great for your rogue when he gets into a pinch.
This is a really good way to give your players the edge in the long run, especially if you are unwilling to drop high value items.
Be generous with traits
This could be a houserule or just a favourable interpretation of the rules but one thing I do is allow players to get a new trait every level and ignore the limit on how they cannot have more than one trait per "list". Considering there are over 1000 traits and normally players can only pick two of them at the beginning of the game that makes this a rather untapped resource.
It can reflect how the PCs have been developing as characters in acquiring new traits. This can do a huge amount to help keep them viable despite such a paucity of wealth.
Best Answer
D&D is a rules set, not a setting. Therefore details like this are never RAW, but they may be described in a setting. For example, if you play in the Forgotten Realms, there may be some canon as to the availability of banking there. If it's your/your GM's own world, then it is completely up to you.
In most fantasy worlds there's not widely available normal or magical banking; even in high magic settings it's usually at best local storage. Throughout the years of D&D, PCs generally:
Frankly, #4 is by far the most common. PCs hate letting their money out of their sight and magical items that carry loot are common enough they usually don't have to.
Now, for one positive example in the Pathfinder world of Golarion there's a god of money and such and his temples are banks. IME PCs don't use that much either because, you know, what if you have to waste one of those priests one day, you don't want your money confiscated... And if you want to research real-world early banking and implement it in your game, hooray for everyone learning something. But it's all in your purview as GM.