Preflop
KQs is correct to open and call a 3-bet, and AQo is correct to 3-bet. Maybe there is some argument for folding KQs to a BB 3-bet, since most players have very few bluffs from this position, but the GTO line is definitely to call.
Flop
AQo is correct to go for a C-bet, since the preflop 3-bettor usually C-bet more or less range. KQs is correct to just call with a draw, since we often lack fold
equity in 3-bet pots, and KQs has position.
Turn
AQo pick up a gutshot and a decent "scare card", so seems like a reasonable situation to fire again. However with only around a pot sized bet left, there is not enough stack depth to make this a 3-street hand, so AQo need to either jam or check here. KQs is correct to call again having now improved to top pair and still with a draw to back it up.
River
With just 1/3 pot sized bet left, and the flopped top pair becoming trips, AQo lack fold equity and need to check with intention to check-fold. KQs is correct to call the jam getting around 4:1, and should have checked back if checked to.