Ok so lets talk about villain first and make a plan from there.

Villain is 38/0, he slowplays big hands, and is known to be passive otherwise.

So naturally, we expect him to be either calling and folding with weak value hands and apparently also either call or raise with his nut hands. Generally, since he is so loose pf, hes going to have a very weak range made up of mostly air regardless of the flop.

So with that in mind

The AT4r board...

Our plan here with TPGK is going to be bet folding every street. Villain can easily (and we expect him to) call down with Ax or Tx or like QJ KJ if we bet. We also expect him to call/raise any hand that beats us at some point in the hand as well.

If villain instead were to lead out at some point, we probably switch to a more passive call down and bet if checked too kind of line because we'd expect him to some to lead some hands that we beat a lot.