just a question : where are you playing?

His range appears to be only pp hands and AT/KT
I think a livetard would bet the flop with any pairs, just being afraid of a check behind, thinking he is playing against broadway hands. Generally speaking livetard always thought we have AK in hands when we 3 bet. On the flop I don't think he would bet TT or x2 Hands.

As he 3 barreled with lower bet sizing I think his range is polarized : pocket pairs or full (with 33 or 44). His bet looks like a value bet OR a blocking one (even if the sizing is a bit high for a blocking one, he maybe just want to avoid a shove).

I like your line, would have played the same flop & turn.
Now OTR I don't think he would fold 66-77-88-99-JJ if he bet with those hands on 3 streets.
So right play on the river would be : jam>>fold>>call, even if it is hard to fold if you called the turn.

As played I would shove river.

I would play the same way and hope he comes out with some random hand since he's unknown. He will show a 2 sometimes and maybe AA/KK
hard to fold though
I don't really see how you could have played any different except for maybe folding otr instead of calling, I don't think is a great ev difference though and optimal play has to be calling I would say

Results:

I considered TT unlikely, 2 almost impossible, didn't think he had AA/KK and called. He had KK which blew my mind a little. In hindsight, I think I should've folded river as the triple donk line is very strong. Turn fold would be sick. I played more with this dude later and he's a fish - he doesn't know what he's doing so he often ends up taking weird lines.

If we go by pot odds though, we should prolly call. Pot odds we need only 22% equity. With AT in his range we have 54%, without we have 30%. But I'm not big on pot odds. Live is so exploitative that many lines are so unbalanced that it's a fold regardless of the "pot odds". Meaning, I think we're good here LESS than 22% of the time - no matter how surprising this seems.

Board: Tc 2s 2d 3h 4h
Dead:

equity win tie pots won pots tied
Hand 0: 54.412% 52.94% 01.47% 18 0.50 { QdQh }
Hand 1: 45.588% 44.12% 01.47% 15 0.50 { TT+, ATs, ATo }

equity win tie pots won pots tied
Hand 0: 29.545% 27.27% 02.27% 6 0.50 { QdQh }
Hand 1: 70.455% 68.18% 02.27% 15 0.50 { TT+ }