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It would be awesome if Saved Instances would remember all your characters' great vault activities (or just that they did something) and accordingly show the next week which characters have great vaults to open. This is for people who have a lot of characters and can't remember which ones they ran m+ on, or who forget to loot the vault later in the week because they were thinking about it, etc.

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Alter Ego does say it does this: https://www.curseforge.com/wow/addons/alterego "Track your Great Vault progress and get notified of available Great Vault rewards." But would prefer to not have to add another addon for just that one feature.

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What you are asking for does already exist in SavedInstances, although not clumped together.
If you take a look at the picture below (sorry its one of my toons so it is a little messy), you will see that there is something called dungeon runs where it shows "H|H" that means i have the first two vaults open on an heroic level. Mouse over will also bring up a window thats shows you the level of dungeon done.

Similarly for Delves, it will be shown under "World" and will show you what level of vault it is, say you have done delve 8s then it should show "8|8" for two slots of 616 gear.

I dont raid end game so i cant show the raid one.

Also, on the following week, if you have yet to open the vault, it will show a yellow ? instead of the numbers.