Ability Cooldown Not Saving

I would recommend making the cooldown a number tag instead of logic. Then check if it is = 0 instead of if it is false, setting it to 200 instead of setting it to true, and removing the wait block and resetting it to false from this procedure.

Then create a second procedure that activates on item tick update, where if the tag is > 0, setting it to itself - 1. This second procedure will act as an item-based cooldown that will allow the item to cooldown from anywhere in the player's inventory.

Alternatively (and this may not be what you want, and it would only work for a shared cooldown across all abilities and all items of the same type), Minecraft has a built-in cooldown system like what is used for ender pearls, you could use that instead of data tags. MCreator has a procedure block to set an item on cooldown and I'm pretty sure one that checks if the item is on cooldown, so you could use those. An upside is that it would display a visual cooldown overlay on the item, downsides are that you would need to have one cooldown for all abilities, and it would also prevent right-click uses of the item. And another thing about the vanilla Minecraft cooldown mechanic is that it is player-based rather than item-based, so if you have two of the same item, they would both go on cooldown.

If you like the first method but want the player-based cooldowns (so a hotbar full of the same item only lets someone use the ability once within the normal cooldown time, rather then being able to spam it nine times), you could use a global variable with the scope of player persistent of player lifetime, instead of using a number tag. And for the second procedure, have it use the player tick global trigger, rather than the item's in inventory tick trigger.

Hopefully this helps.

Yes, "when tool in inventory tick" is the trigger I meant to say, I just forgot the name.

It looks like you almost have it, just one thing you need to change in the second procedure. Instead of setting the tag to 1, there is a procedure block that lets you do mathematical operations (I think it defaults to +, but you can click on the center of it to change it). You can use that procedure block to set the tag to itself (by using another "Get custom data number tag" block, the operation block set to -, and the 1 you are already using).

Yes, that's what I meant.

It's been a little while since I've done something like this, so I forgot about the first problem, but, yes, that's happened whenever I've done this method as well. Maybe you could try using the player variable method I mentioned in my earlier comment, but that would make the cooldown per-player rather than per-item, which might not be what you want.

The second problem is really weird. I'm not sure what's causing it, but it could be a client-server desynchronization issue, because those cause a lot of weird bugs. If it is a client-server desynchronization issue, it can be solved by putting the whole procedure in an if statement that checks "If" "Not" "Is provided world client-side". But if that doesn't solve it, I don't know how to fix it.

I realize now that I didn't explain it well, but you could use multiple player variables, one for each ability. They would be player-based rather than item-based, but you could still have multiple abilities, unlike the vanilla Minecraft cooldown mechanic.

No problem, I'm glad I was able to help.