This is a combination of history and what appears to be a small but significant oversight. The advantage of the Haversack over the Bag has always been that the Haversack always has what you're looking for on top, as compared to the Bag which is a disordered bag of stuff that's harder to sift through the more it holds (and it can hold so much).
The designers appear to have retained this distinction in the items' described function, and then made it immaterial during development by copy-pasting the standard 5e item-interaction boilerplate into their descriptions without making any adjustments to implement the functional difference they kept in the descriptions. (Easy enough to do, since when you're doing the rules polishing on the Bag you're not thinking about the Haversack, and it all looks fine, right?)
Traditionally (I mean back in AD&D, since in 3.x this is likely the kind of thing DMs would just handwave away), digging through a Bag for an item wasn't feasible during combat, so the discovery of a Haversack was a significant upgrade in, well, handiness. The capacity difference meant neither was strictly superior, but each had different pros and cons (the marginal utility of being usable in combat making the Haversack especially desirable, but still not strictly superior in every way). But none of this was nailed down in rigid action-economy terms then — there was no such thing as strict action economy terminology, it was just how the items' descriptions said they worked. The rarity difference in the 5e items appears to reflect a design intent to limit access to the especially-desirable item usable at combat speeds; later negated by failing to implement this small but significant distinction during the development stage.
So it just seems to be an oversight. RAW, the Haversack is the clear loser. For many DMs, the question ends there (plus a bit of head-scratching at the designers). However, 5e DMs aren't bound by RAW and are encouraged to make 'fluff' matter in their games, if they so desire.
If you want to emulate the traditional utility of the Haversack, make Bags of Holding able to be interacted with using an action... but it takes multiple before the user finds what they're looking for. You can either nail this down (at which point you're into making house rules to taste to determine exact number of actions), or just say that it's only possible during non-combat time and handwave the exact time it takes. No matter how you implement it exactly, this will leave the Haversack as the true champion of handiness that's usable with a single action to get exactly what you want.
The answer to this question can't be found directly in the RAW, so we must engage in some speculation, specifically the success of the action hinges on what you see when you look into a Bag of Holding and what you see when you look out of it. Let's look at the descriptions:
Misty Step:
Briefly surrounded by silvery mist, you teleport up to 30 feet to an unoccupied space that you can see. (PHB pg. 260)
Bag of Holding:
This bag has an interior space considerably larger than its outside dimensions, roughly 2 feet in diameter at the mouth and 4 feet deep. The bag can hold up to 500 pounds, not exceeding a volume of 64 cubic feet. The bag weighs 15 pounds, regardless of its contents.... Breathing creatures inside the bag can survive up to a number of minutes equal to 10 divided by the number of creatures (minimum 1 minute), after which time they begin to suffocate... (DMG pgs. 153-154).
As you can see there are several requirements that must be met for you to able to accomplish this action:
You must not put the weight of the items inside the bag to over 500 lbs, meaning that you must add your character weight, items you are carrying, and items already inside the bag to see if you exceed the weight limit (if you do the bag breaks and its contents are set adrift in the astral plane!).
You must not stay in the bag for more that 10 minutes (assuming your the only one in there) lest you suffocate.
As per Misty Step you must be able to see where you are going- which is where the speculation begins.
Since you have to see where you are going, you will not be able to teleport into or out of a closed bag, but if the bag is open and you can look inside you might be able to justify the this action (similarly, if you can see out of the bag when inside). So basically what it comes down to is the description of what you see when you look inside (or outside) the bag. Since no official source (to my knowledge) contains such a description it would be the DM's call. If you can see a tiny storage room with all your items or even a sea of floating items you could probably justify using misty step, but if you see blackness, a void, or even just an empty bag you can't use Misty Step.
In conclusion - Maybe, it depends on whether or not you can see into or out of the open bag's item storage area (I'm hesitant to say that it is an extradimensional space b/c it is not specifically stated in the RAW) which is dependent on how your DM describes the bag. However, even if your DM excepts this justification, it may be much easier for you (depending on your size) just jump in normally.
Best Answer
Nope, for two reasons.
First, simply because the contents of the bag aren't held in any kind of stasis. A fireball spell is somehow put in? The spell of duration “instantaneous” is over now. It won't be there later, “waiting” to be brought back.
So what would happen with successfully (see below!) chucking fireballs in, is burning up any flammable contents of the bag (they're unattended, sitting there in the pocket dimension, and won't benefit from the PC's own saving throws, after all), and the fireball being done. Opening the bag later will just have… nothing… happen, while the intended target of the fiery destruction looks at the bag-holder funny.
(That's assuming that filling a bag of holding with fireballs doesn't count as the bag being “overloaded, pierced, or torn”, which would additionally spread the contents' ashes across the Astral plane.)
Similarly for other spells of instantaneous duration.
But that is only the least of the hurdles to overcoming this.
The second, more important problem is that the bag doesn't permit free-flowing movement between dimensions anyway, so spells can't be cast into it in the first place for lack of line of sight. The trouble is that the bag's mouth isn't a portal that allows free passive movement of items/air/material/explosions between the bag-owner's dimension and the pocket dimension. The mouth is a magical surface of some kind that is activated only by a creature actively putting or taking objects. (Notice that an action is required to add and retrieve objects, and that the contents of a bag won't spill out if you turn it upside-down.)
This means that, even if a spell is somehow successfully cast “into” the bag (perhaps the caster jumps in briefly?), something like a delayed blast fireball or a similar injurious spell with a convenient timer won't “spew” out of the mouth of the bag at the determined time. Instead, such spells will just take effect in the pocket dimension, never passing out of the bag.