Open AK, call the 3-bet, mostly call flop, then just call river versus the shove.
Flop K♠9♦2♣ is very favorable for us: we have top pair/top kicker on a dry board with SPR still around 2.5. BB leads small for 8BB into ~32.5BB, which is a small probe into a big pot. Solver prefers calling AK here most of the time, with some large raises to pressure 9x/2x and weaker Kx. By raising to 24BB, we’re targeting those medium-strength hands and making it expensive for them to continue.
Turn 7♥ is a complete brick for our hand; we still have top pair/top kicker. After we raise flop and get called, BB’s range is weighted toward strong Kx, 9x, and some slowplayed overpairs. Checking back here is perfectly reasonable—our hand is strong enough to win at showdown, and betting into a condensed range would mostly get action from better hands.
River 4♦ is another brick, and BB now shoves 57BB into ~137.5BB. We’re getting about 2.4:1, needing ~29% equity. AK is still ahead of a lot of bluffs (some missed draws, random floats) and some weaker Kx that might not have raised flop. Calling off is standard; folding would be too tight.