First of all. If I don't have any read on my opponent I wouldn't 4b AQ, you will most often come to a difficult decision when you don't hit the Q. And because of the 4b you have narrowed his range to a lot of hands that got you beat.

If I 4b tho I will come out with a half pot bet on the flop. Just to see how he is reacting. if he is sitting there with something like AJs or QJs or maybe a middle par you will put him in a difficult spot. If he raises its an easy fold. If he calls you could bet the turn also if you feel that you can hit him off the pot.

Tho when you check the flop i don't get the turn bet. The deuce does nothing to the board and can't possibly have done anything to your hand. When you bet it, it seems like you are just trying to put an aggression on my flop check.

Thats just my two cents.

When he 3bets an utg raiser and calls the 4b with a player still to act his range is very strong (JJ-KK, AQs+ imo).

Vs this range I rather cbet flop and give up when called. This is more likely to fold out JJ QQ than a delayed turn cbet.
River is a good x/fold as the only hand you hand make fold is maybe QQ.

Would you just fold this pre then and not have a 4bet bluffing range at all vs unknowns? I mean, I don't think we can profitably call this pre unless there's a confirmed weaker player involved...

Concerning post, I don't mind my line too much because I'm pretty convinced it achieves close to the same vs various parts of his range but I'm probably still better off betting flop and jamming turn if I plan on 2barreling this. Fwiw I don't think he ever folds TT-QQ to a single flop bet.

Against 2 unknown I don't see this as a great spot to call AQo pre so IMO I'd be more inclined to fold.

As played I think you can 4bet a little larger here since you now have 2 in the pot and by raising smaller CO will be calling you wider. IMO 31-33bb would have been a better size for your 4bet.

Flop - Checking this flop looks really weird after a 4bet pre. Read weird as a total miss. I'm Cbetting pretty much 100% of the time for 1/3 psb. .

Turn - Great turn card for us as it does nothing for villains range. Barreling 1/2 psb after Cbetting the flop. But betting on a 2 after checking the flop looks even more like you 4bet wide, missed the flop, and aren't really sure where you are.

You have the right idea that calling against a 3bet with a cold caller is not the optimal play. The best play is to fold.

4bet bluff AQo sparingly vs a BTN 3bet only is a profitable play but I don't think it's a profitable play as a 4bet squeeze vs a villain who 3bets vs UTG and a villain cold calling 3bet OOP especially at 10NL. But I prefer the 4bet squeeze more than calling.

So when he calls the 4bet, his range is JJ+, AK but maybe he folds AK, JJ, maybe even QQ because of the person behind and your nutted range.

Flop: I think check folding is fine. I would check my entire range here including AA, KK.
Villain should also check back his entire range here too. Betting denies your opponent a chance to barrel and you can always get value later. You see some people value bet here, so you can just simply fold and not have to burn money barreling.

Turn: I like betting half pot here too. Bottom of your range. Line makes sense when you have AA/KK. You don't beat anything villain should have and could potentially fold out better hands.

River: You can go either way with checking or shoving. One of those gray area villain dependent spots. With an unknown at 10NL, probably leaning towards giving up. Can't rely on an unknown at 10NL to fold AK.

Actually, having thought a bit more about this I'm starting to think cbetting flop is a mistake. Again I'm not 100% sure about pre but I'd tend to flat at least most of my AKo combos preflop which should provide CO with a pretty clear range advantage OTF, especially if I put some bluffs into my 4b range.
Seems like I somehow intuitively followed this thought ingame.

Fold pre