OK so a couple of things. I like the squeeze here, because it is a hand that hits a lot of flops, you just don't want to go with it multiway OOP so that is why I like the squeeze to get the hand preferably HU so you have to worry less about your hand not being so nutty. Unfortunately you still get both players in but if this was your idea behind the raise to cut down the field because in a single raised pot, OOP and MultiWay, your hand would not perform so well and thus you try to create a 3bet pot (OOP) but at least HU, I would agree with this reasoning. And yes you can Cbet Axx imo if you don't play your hand but your range here, and you range should indeed include quite some Ax and even AA hands (most people will actually perceive you to have AA after a SB 3bet). So I would say that Cbet is ok. But you get called by two players, and then I would slow down. Then on this 6h turn you check, and now BTN fires full pot, and you call and CO folds. Now because he fires full pot, it looks very much like a valuebet that is protecting against draws on this board (flushdraws and full house draws) and on a A87r board, my guess a lot of straightdraws around the 78-connectors are indeed in his flop calling range.
Now the thing is, you are wondering if you should have Cbet turn as well as the H is good for you you say. But since you are 3way and 1st to act, you don't even know if your flushdraw is live, and the rank of the turncard (6) is not good for you but helps calling ranges more. So I don't think betting achieves anything here and bet stackoff after you get raised will see you stacking off with at best a live flushdraw with a gutter, which will give you around 27% on average but there is no fold equity here I suppose (fold equity means you make a better hand fold, but you could well but up against the nuts here someone playing 9Tx and you won't make the nuts fold).
The only problem I see with you calling a full PSB here is that you need to have the implied odds here to make the call on turn if you decide to call. Now 2 thoughts come to mind. If BTN had nuts + flush-redraw, my bet would be he would bet a bit less than fullpot as he would have less to protect against. About the CO, and now you see the problems related to having to call now on turn before the CO, is that the CO could theoretically still have the NFD here. But he folds turn, and of course he could fold the NFD here but I think that now you are HU, you don't have to worry so much anymore about your Khi flushdraw being nutty or not (considering the fullpotbetsizing range of BTN here), I would always consider it to be live after someone reps the made straight, and the other player that could have the nutflush draw folds.
However, if you look at your stacksize, you started the hand with around $21 but now you only have around $10 left and you would then need to get an OOP donkshove by you once you make your hand (if you had had ony 25% equity you need to get $8.35 on implied odds called on river, so here probably a bit less) and I think it is just too unlikely that you will ever cash in on your required implied odds, for several reasons:
a) you are first to act OOP which means you have to donk/shove
b)you have to donk big (you need to have your donksize * number of times villain calls on average = your required implied odds)
c) the flushdraw is generally a large part of calling range here and is obvious when it hits meaning you won't be as likely to get paid off
e) the T is less obvious which thus has greater implied odds but this is a 3 outer.
Now the only thing I thought was superinteresting was the endresult. The guy checks back river, which tells a lot about your perceived range in this hand. He makes a boat, but does NOT valuebet river here even though he beats all flushes that might still call a bet. But no he checks behind because he actually felt that AA was still in your (perceived squeeze from SB-)range here (apart from a misclick this is the only explanation I see for his checkback)!
GL
Q
K
(3 players)
