You said "I should have bet the turn, *I guess.*"

That is equivocating on what should have been a slam dunk decision for you, so it is beneficial for you to hear that the turn is a bet 10 or 20 times.

I don't mean to be late to the party, but I can't think of any reasons to check turn ever. Like literally 0. Bet and get that stack

Get that stack how?
Do you really think he is going to pay off 250BB with an overpair? We resulted in gaining 84BBd from him.

Furthermore, his cold calling range in this spot is going to be most PP and AK/AQ. His 4bet range in general is 2.05% (AA/KK/QQ/AK). However, given the fact that we are 250BB deep, and with a 20/13 style I don't see him 4 betting here oop with anything less then AA or KK and on a rare occasion QQ, thus resulting in a even bigger cold calling range.
The way he plays the hand it looks like a 10-10 J-J or Q-Q hand, however he could also bet 6-6 or 7-7 or on occasion AK the on the flop.
Given the fact that he will never call a turn and a river bet with 10-10 J-J or Q-Q we give him on the river an opportunity to bet and potentially bluff into us and extract top value.
Secondly, if we bet turn I don't see him ever shoving over us with a hand which does not have us beat. He does not turn an overpair into a bluff there, period.
However, valuable information would be %donkbet + WTSD and Won@SD.

bluff more if you really believe you never get calldowns from TT-QQ on this board.

Ofcourse!! However, I don't see many nl100 regs turning a hand in a bluff 250 BB deep!!

bet turn/bet river. Just call as played