We can asnwer this question of river calling if we know who we are playing with. I think that depending on villain profile we could've made a 3-bet preflop, because button opens a lot of
hands and AQ is not a huge hand to try to trap preflop. Villain will own plenty of dominated Ax opening from BU, but when we simply call from the blinds we have no idea where we are. We must assume all combos for villain, including AK and AA, so what's the point of calling with AT, AJ and AQ?
Personally I'm more inclined to call more often from the blinds versus button when I own AK. But AQ most of times is a 3-bet preflop, and this regardless of player profile, whether this is a NIT, a tight regular, a passive recreational or a maniac recreational.
Because when we call preflop we must already have a plan for flops that miss, for flops that hit like this one and villain bets, we must have a plan like "if we are calling on the flop is because we think we are ahead and we continue calling on X, Y, Z cards, fold to A, B, C, D, cards and raise to 1, 2, 3 cards. Even if it comes Omega, Sigma and Beta cards our plan is to fold. We must have this plan on our mind before calling because we believe we are ahead.
In this case we thought we were ahead and we called preflop. We called flop. We called turn. To simply give up the hand because it completed a flush.
I think that most of times in a situation like this, on the flop and on the turn we are way ahead of villain and we could check-raise to protect our hand and make value out of it: villain might continue paying with flush draws, gutshots, dominated Ax, and even try to defend weaker pocket pairs because we are in a blinds versus button position where ranges tend to be wide.
The point is, if there is a mistake in this hand, it began preflop, when we flatted AQ instead of making a 3-bet and taking initiative upon the pot, upon the range and upon our opponent.