Calling an undersized 3-bet with ATs is definitely reasonable even out of position. I am not loving it, but for this price you gotta put in the money and see a flop.
Why are you donk betting (leading) the flop? Yes you flopped TPTK, but if he has, what he is representing by 3-betting, it does not really change anything, because then he has an overpair. JJ, QQ, KK, AA are a big part of his range. He could have AK, AQ as well, but then he is just going to fold, so you win nothing extra. Checking to the preflop raiser is the only play, that should ever be made here.
Checking the turn is definitely the right play, I see no reason to donk bet again. He checked back, that is great, maybe he was
bluffing, and now he is looking to give up. I see no reason to jam the river. You should check again and probably check-fold, if he jam. AQ got there, so now you pretty much only beat AK and a complete
bluff.
All that being said this guy look like a goofball. Silly undersized 3-bet preflop, and then he makes another silly mini-raise on the flop but check back turn, when you check. So I am not really quite sure, what story he is telling here. It seem to me, he might just be goofing around with some silly nonsense and clicking buttons. But that does not mean, you can jam the river for value. If he have some kind of missed draw or AK high, he is not going to call you with that.