Preflop
This is already a very awkward spot with a 3-bet ahead of you, and as I understand it, even the best players in the world dont agree, how to handle the situation. Based on the player info I do lean toward cold calling the 3-bet though and not putting in a 4-bet. The reason is, you want the fishy player to come along with whatever, he has, and by just flatting you are much more likely to achieve that result. Giving the fish an easy way out and then getting called by the reg is the worst possible outcome, and you can take that option off the table by not 4-betting.
Postflop
There is no way around the fact, that this spot is just super awkward, and I dont actually even know, what is the theoretically correct way to proceed. The issue is, the SPR is just so low, and ranges in 4-bet pots tend to be very narrow. I guess, you can still beat AQ, but that hand is not going to give you a lot of action, if you continue firing, and you lose to everything else, he can reasonably have. So while this might not be GTO poker, I would probably just look to check-fold already on the flop.
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