Fold without a second thought. Versus a 3-bet that big you have no option to flat-call given the stack sizes (although you still wouldn’t really have the option to flat-call here even if you were a lot deeper), and you have no fold equity on a 4-bet. Villain’s range is likely very heavy on AK/TT/JJ in a spot like this so your raw equity isn’t good either. It’s totally fine – and in fact necessary – to fold a large portion of your range to a really big 3-bet like this. Just dump it.

I think the stack depth at 200/400 where I’m considering flatting a 5600 3-bet OOP with anything after I’ve opened to 900 is probably something around 60,000 (since villain’s range is so strong and there’s >14k in the pot after we call), and the stack depth where I would consider flatting AQo is probably…100k? 120k? Not really sure. Even at those stacks I feel weird about it considering AQo plays so poorly OOP against tight ranges. AQs I would probably flat at 60k since it’s a bit easier to hit flops with a suited hand, but that’s a massive 3-bet no matter how deep you are, and villain’s range is still super strong.

I don’t want to say you’ll never see this thing in higher buyin tournaments because there are still weaker players in those tournaments, but this is not something you’ll really see from regs/good players at any level. It’s virtually impossible to create a strategy where 3-betting to 5600 from a 13k stack is good because you’re priced in to calling off your stack with whatever you have once the raiser shoves, and yet the kind of hands you would be okay with doing that are losing a ton of value by 3-betting so big.

Try not to make such a big distinction between ‘higher buyin players/lower buyin players’. There are a lot of bad poker players who have the money to play higher buyins, and these days there are some somewhat decent (if usually very nitty) grinders playing even very low stakes games.