4bet/get it in pre might be better. Calling is fine too.
Turn is super gross. Just addressing raising vs calling, I know it feels like you should just call, but he never has bluffs here, you're never not calling off on the river, and he might be able to puke fold AK if a heart comes and you shove. So if you're continuing with the hand then I'd jam.
As for jamming vs folding, it's close. You're getting it in for 34.5% of final pot and your equity against { AA, QQ, 99, AQ+ } is 32.5%. So that would be a small loss. That seems like the "normal" range that a player should have in this spot. Is it possible AK isn't in some people's turn betting range? idk. It feels more likely that this guy is a psycho and has like JT or AJ or something. It's close enough that I might base my decision on some kind of live read, like WARNING RACIST CONTENT:
I think any action is OK tbh, it's just a marginal spot. Everything feels gross because everything is gross.