Give them a better idea of the threat level
If you are playing a sandbox style game, it is up to the players to determine what level of known risks they wish to face. Thus, you probably do not want to telegraph too strongly that you think they are ready; that decision is up to them. Dice have vagaries and players play with differing levels of tactical skill and system mastery and character optimization. Unless you plan on using a deus ex machina to put your thumb on the scale for one side or the other, you only know how deadly an encounter is meant to be, not how deadly it will actually be. So, in a sandbox style game, let them figure out how much risk to take. Just give them a fair idea of what those risks (and possible rewards) are.
In your dragon example, they can meet someone that can tell them more about that specific dragon's capabilities and thus judge for themselves if they wish to face it. One indirect way to do that is to tell them more about the last adventuring party so they can say "Yes, we are more powerful than that now".
Put the encounter on a timer
One way to encourage the encounter is to do something to make it urgent. If something bad happens if the issue is not resolved within a time limit, they will be much more motivated to find a way to resolve it now. From any but the most ruthless or most dedicated to a "breathing world" GM, this will also be a not-so-subtle but also not meta-gaming signal that the GM thinks the encounter can be resolved within that time period.
Perhaps the dragon is now threatening a town by demanding a major payment of tribute within a week or it will attack. The adventurers now have a deadline to resolve it or the town will be directly harmed. They won't even be able to say that they can get the tribute back from the dragon later when they are yet more powerful, if much of the tribute is in the form of consumables like cattle that will be eaten. Or, if you want to be more cliché, perhaps the demanded tribute includes a hostage.
Fix it in the real world
You're already basically off of RAW with a +4 weapon. 5e RAW only has +1 through +3 -- the Moonblade artifact even specifically calls out that you reroll if you roll the 'increase bonus' rune and the weapon is already at +3.
But laying that aside for the moment: This isn't a situation you can really solve in-game. You need to have this discussion outside the game, player to player. At least some of the players are already unhappy with what's going on, so this is the time to stop thinking of yourself as the sole arbiter of the game, and collaborate.
If you try to fix this by fiat, all you're going to do is upset your friends. Putting together a plot that ends with the moonblade and other powerful weapons lost, destroyed, or depowered is fine -- but you're going to have to get player buy-in for that first.
Have a discussion with your players. You don't have to work out plot details, but talk it over. Figure out what THEY are willing to do. Lay out the problem, and ask for suggestions. Not everyone will be excited to lose their cool gear, but only the most childish player will absolutely refuse to give up their awesome sword if it really is causing a problem with the game.
First off, realize that 5e is designed so that nobody NEEDS a magic sword to be perfectly capable. A +2 to attack and damage is nice, but not necessary. It's really not a big deal to be a 7th level fighter with a plain old steel sword. Your damage output is going to be only slightly lower than with the sword. If you really want to get a magic weapon into the Eldritch Knight's hands, that's fine, just let him use a standard weapon until it's narratively appropriate. There really shouldn't be any rush.
For the rest, the easiest answer is to just retcon the overpowered weapons into less powerful, but similar, weapons.
For the moonblade, I assume you rolled it as specified in the book, with d6+1 runes, with the first giving it +1 and the rest rolled on the power table. If so, then maybe the player will be willing to hand-wave away a few runes. If you rolled 6 runes initially, and it's messing stuff up, maybe your player would be willing to cut it down to 3 runes, with only the initial +1 giving it the damage boost, and the others giving powers rather than more plusses. Just retcon the whole thing to a less powerful version of the item, agree out-of-character that it's always been that way, and move on. (Moonblades are specifically useful that way since they can scale.)
The holy avenger might become a slightly less powerful 'holy sword' or some such thing, say a +2 weapon that deals +1d6 radiant damage to fiends and undead, but doesn't do the whole save bonus thing.
I don't know what a Zariel's cursed sword is but I imagine you can do the same sort of thing there.
If you and your players are unhappy with a simple retcon, then I'd suggest going the route of coming up with a reason the weapons have to be relinquished or destroyed, but again, you need to have at least some part of that discussion at the table, not just spring it on the players. In this situation, I'd collectively come up with a story that you can all be happy about, and then play it out (rather than you as DM running off to plot and plan and come up with a surprising story) -- but if you really don't want to do that, at least get player buy-in on you going off to develop a plot around removing the weapons in some way. If you end up destroying the weapons, it might be worth it to let the players keep some shards of their original weapons (or some such thing) that let them forge weakened versions of the weapons, as I discussed above.
But I suggest getting the players to help craft the story of why the weapons are gone (if you don't just retcon them). That's how you keep the players happy -- because what's happening isn't being done to them, but by them.
Plus that avoids the biggest problem with a fiat removal of the weapons -- somebody trying to weasel out of it. Worst case, somebody manages to succeed at a roll or comes up with a plan you didn't expect, and you're forced to concede that they managed to save their weapon from destruction, which negates the whole point (often supported by liberal use of 'My Guy syndrome' -- "My guy wouldn't just let that happen! He tries to escape!"). If the players made up their own fate, there's no motivation to try to dodge it. It was their own story.
Best Answer
This is a "Multipart Encounter"
In your case you've got two immediately-sequential encounters:
First of all, let's note that for your party (4xL7, 1xL5) even the dragon alone would be a "super-deadly" encounter. That's my term for an encounter that would fall in the "deadly" threshold even if all party members were one level more-advanced!
But when we turn to "Multipart Encounters" we get another delightful little gem:
Your adventuring day budget for (4xL7) + (1xL5) is 23,500 XP. (DMG p.84) This two-part encounter has an adjusted XP value of ~11,000 XP.* This two-part encounter's going to play even harder than a cake-walk followed by a super-deadly encounter. Therefore...
The dragon should easily kill your entire party.
It would have done so on its own. The half-dragon just might have tenderized the meat a bit.
* - I've halved the half-dragon's XP value, isn't quite right, but it doesn't matter in the slightest because the dragon alone is already 10,000 XP--well beyond the "one-third adventuring day" threshold!