Preflop
Standard open.
Flop
Check-calling with bottom set is pretty much as passive, as it can possible be, and I am not a fan of it. Yes a flopped straight is possible with T8, but they likely only play T8s, and even if someone has that hand, you still have 7 outs for the board to pair on the turn and 10 on the river. Maybe a check-raise is bordering on an overplay, especially in a multiway pot, but I definitely prefer to bet (and be willing to call a raise) rather than check, and I would go larger, than the opponent did. Maybe 2/3 pot or something.
Turn
There are so many draws, you want to charge on this board, and so many river cards, that could potentially kill the action. So even as played I kind of want to bet here, even though this would now be a donk bet. But at least the opponent made a sizable bet for you, and as played at this point I would just call.
River
Now the frontdoor flushdraw came in, and the KT gutshot came in as well, so this is definitely not the best card in the deck for you. If you had kept the betting lead, you could consider a moderately sized bet for value AKA "blocker" and then fold, if you get raised. But donk betting on this card would be pretty weird and almost overrepresenting your hand, since the hand, that would most commonly take such a line for value, would be a flush.
So as played I do think, the correct option is to check again. And just to make the analysis complete, my plan would be to check-call most of the time. Maybe if he make some massive overbet, I can find a fold, but against any sort of normal sizing I think, you beat at least some valuebets like for instance QJ, and then its pretty much mandatory to call.
Results
I dont think, there is any chance, you could have stacked him, when he had a top pair type hand and started with almost 100BB. At least not if he is any type of player. But I think, you could have won a bigger pot and made his life more difficult by maintaining control over the hand instead of handing it over to him.
If I was in his spot, I would probably have played KJs the exact same way, he did, apart from potentially 3-betting it pre. And when I check back the river, I would expect to sometimes win but also sometimes lose. But I would be shocked to lose to a flopped set, that was played this way, and I would feel, I lost the absolut minimum in the hand.