RFI and 3B stats can be pretty good indicators of aggression but tough spot. Being so deep could we consider checking turn after no longer having nuts in multiway pot?

Yeah tough spot. Makes sense for SB to get to turn and river here with plenty of filled up Jx hands. I would somewhat discount QQ and TT but would still give them those at some frequency.

Just doing some quick combinatorics:
TT - 50% = 1.5 combos
QQ - 50% = 1.5 combos
JT- all combos = 6 suited only = 1 combo
QJ - all combos = 6 suited only = 1 combo

Analyzing the river shove - if we give SB all these combos they have 15 value combos that beat us.

We need to call 10536 and total pot will be 43657 so we need 24% equity. So, villain will need 25% roughly of their bets here to be bluffs for us to call.

Therefore, villain needs at least 5 bluff combos to make this a call (5/20 = 0.25). VIllain can also have thin valuebets that we beat to make up these combos, but I doubt that they have any value bets that we beat. I also have a hard time thinking of what bluffs villain can have. With us blocking Ks it's hard for villain to really have any flush+str8 draw hands that they go off with. Therefore, I think the river is a fold.

On the turn, we need 27% Equity to call this raise - this can be determined by analyzing hand vs. range in a simple equity calculator and playing around with villain's range. Turn is closer than river IMO as it is more plausible that villain can have combo draws/ some Jx + OESD, etc. However, villain still has all those 15 combos of nutted hands on turn as well. It's a close spot that is highly dependent on villain's range construction (how often will they semi-bluff Jx + draw mainly). Vs an unknown I guess you can default to a pseudo-GTO strategy, and without running a sim I would guess that GTO strat would not be folding this combo here very often.

EDIT: I also agree that checking turn has some merit but have no idea which is better in theory. Also, if you think SB never 3bets TT, this is a worse spot for you since they would need more bluffs to make calls OTT and OTR profitable.