Assuming GTO strat, I open UTG 6max with 8732 and BB defends.

3-1, xbc (I make 87632)
2-Pat xbc
1-Pat x....

From both sides of the hand what is the thinnest bet you are making v BB/what is lightest call you are making as BB when bet to?

UTG: I'd guess this is right on the cusp of being a vbet vs a x/b. We have to consider a x/r from BB, if he's playing optimally, so I'd prob lean towards x/b.

BB: Shouldn't be snow-catching too light, based on the EP open, which reps a strong D1 range that should almost always benefit more from drawing than from snowing. We could call down, lead, or xr 96+. The bottom of that range serves as snow-catchers. Some hands should x/r, both as value and rarely, as bluff.

These are just guesstimates, based on the assumptions you provided. In reality, some people will snow-catch w any J/T/9 just bc they are correct to snowcatch w these hands in other spots. But this is a strong line from UTG and BB can often expect to see an 86 or better when UTG bets the river. So it doesn't warrant a light snow-catch.

Conversely, many people in BB will not make optimal river decision when they make a 96+

Thoughts from a learning 2-7 player:
UTG: betting any 8 for sure, maybe betting some good 9s because...
BB: our line could have a fair bit of snows in it as we have the huge range advantage after the first draw, with the EP open and after 3/1 then a draw 2 on the 2nd pull.

I don't have any real experience with GTO in 2-7TD. But I'd expect we need to vbet pretty thin so we can have all those snows and will get called a fair bit because of all those snows.