Getting value on the nut FH.

I think your line was too passive. You must raise either the flop or turn, probably the flop. You are almost certainly ahead otf and villain will have plenty of combos that would call a flop raise. There is a flush draw out there - villain will call Axcc combos if you size properly. Villain likely will call AK combos and certainly KQ.

Alternatively you could use this particular combo to balance your flop floating range and just flat the cbet. If you do then this particular turn card is tremendous for you and you must raise for value. You could be beat but villain feels pretty good about his AK and other Kx combos. Even his FD combos still can call since you are underrepped after the flop call. You set up a nice value shove otr when the flush completes. If the FD misses this is the last chance to get value

agree with this just want to mention that you dont have any need for balance in this stakes so i think flop raise best play.
I think your decision making is to much driven by fear here. Here the fear of him folding and not getting payed that leads to passive plays when having nutted hands in the wrong spots.
Population is not tripple barreling nearly enough with bluffs and you have a hand that is worth all the money on the flop so also this argument makes us to raise flop.
So basicly try to develop a more rational thoughtprocess to avoid emotional manipulation here for example asking yourself how much is your hand worth, how stable is the eq so how easy is it that on the turn or river the board will change so that my set cant go for all the money anymore, is villain bluffing enough etc.

You are right. I probably was engaged in some unnecessary “fancy play syndrome” when I talked about calling otf and raising ott. The flop raise has an added advantage. Micro players almost never three bet your postflop raises as a bluff. If villain should 3! Our flop raise we can probably put him on a range of AA, KK, KQ and (maybe) AK. There are enough KQ combos to allow us to call his flop 3!, but with this particular turn we are now behind all but the AK (if he even 3! With that). I think we could safely fold to a turn bet in a line like that.

What is "3!" ?

appreciate both of your inputs!

I called the flop because I wanted to see if UTG would keep betting so I could extract more money from him. I always like to slowplay and trap people, but that backfire when the turn/river isn't on my side anymore.

In this particular case, I was hoping that he had some flush draw so he could shove.

I rarely deny equity, but sometimes I do.

Shorthand for three-bet. And yes, while there is a place for slow playing, it sounds like you might be overdoing it a bit.