AQs as caller 3bet pot, one card nut flush draw

Yeah man that's really spewy. Your never getting called by worse and when he bets bets on a mono-tone he's pretty much saying AK+.
You have a blocker to the Q so he's not semi bluffing with the nut FD either.

Call turn, fold river.

You overplayed here. What do you want to achieve with this x/shove?
Just call and see what comes on river.

I actually don't know what I wanted to achieve. But I think it was fold out some two pairs and stuff. But they probably wouldn't fold two pairs anyway. Hmm, I can actually see now how standard this play actually should be.

I think if you are going to bluff this, you should check raise OTF. X/shove OTT when you don't improve at all doesn't make much sense to me. I think just calling OTT would be better.

I would check call turn, and hope for spade river. Otherwise I might fold river (depending on the price).