If I am not mistaken you need roughly 26.5% equity vs his shove OTF to break even. If we give him a really wide range for a 4bet that would play this way, such as: JJ+,AKs,AdKc,AhKc,AsKc,AcKd,AcKh,AcKs,AdJc,AhJc,AsJc,AcJd,AcJh,AcJs,AcTd,AcTh,AcTs,Ac9d,Ac9h,Ac9s.

you have 34.77 % equity.

That is obv. a pretty ridiculous range, since not all the hands would shove flop and many would not be always 4bet by villain if ever. Also some hands that might 4bet for value such as AK, would likely not 4bet to that sizing. Therefore, a more realistic range could be:

QQ+,AcJd,AcJh,AcTd

where I added the Ax combos as 4bet bluffs and since he probably doesn't always 4bet these hands I just took 3 combos.

now you are down to 23% equity.

If you don't have any reads, I think it's a fold, even though it's closer than I thought.

PRe Flop FOLD to 4bet with AQ with Stack.

Sorry, i didn't comment on pre. Yes, you can fold pre unless you are against a 4bet happy regular. Like I said with such a 4bet sizing he should be really polarized between AA, KK, and some random bluffs, but i think the majority of players will not have enough bluffs that 4bet to that size to make it worth continuing post.

Also, by folding we can never make a huge mistake, while when calling we will be in plenty of really ugly spots, which becomes really relevant with such a nice stack in a great tourney.

Pot has 24K .. your stack is 12K.
Insta call.

U can fold vs population. Calling cuz of sizing is defendable but ur getting that price for a reason too often, hence def check-back flop and get closer to showdown.