After flop check-raise getting called, the 4s turn gives us a strong straight; we should bet big, around 125% pot, to maximize value from one-pair and two-pair hands.
On T65r we have a gutshot plus backdoor hearts, but no made hand. With a very deep SPR and a draw-heavy board, checking our entire range is preferred. This lets BU c-bet their overcards and weaker pairs while we control the pot with our draws.
Facing a small c-bet on T65r, 87s is a strong candidate to check-raise. We have a strong draw and some backdoor potential, and BU's range is wide enough that a raise is well-supported. Solver prefers a larger raise size (around 1.2x pot) to really pressure one-pair and overcard hands and to set up a river shove.
The 4s turn completes our straight and massively improves our hand. After we check-raise flop and get called, BU still has plenty of one-pair and two-pair hands that are in bad shape versus a straight. Solver wants us to bet big here, roughly 125% pot, to extract maximum value from those hands and to make it expensive for them to continue with weaker holdings.