AKs should 4-bet pre, mostly call flop, and check turn; river we must call the 1bb bet with top pair.
Flop K92 rainbow, SPR ≈2.6: BB has the range advantage on this king-high board, so with top pair we mostly call the small c-bet and only occasionally raise as a bluff. Raising to 22.5bb is a bit too large and too frequent for this combo.
Note: Raising to 22.5bb on K92r is too big and too frequent with top pair; calling the small c-bet is the main line, with only occasional bluff raises.
Turn 7h, SPR ≈0.8: after we raise flop and get called, checking back is reasonable; betting would mostly get called by better and fold out worse. Checking keeps our range protected and avoids overplaying a marginal top pair.
River 4s, pot ≈78bb, BB bets 1bb: with top pair and such a tiny bet, calling is mandatory given the price. Solver also mixes in some jams with AK here, but calling is the straightforward, high-EV choice.