Preflop
With stacks this deep I prefer to go larger than just a min-raise. Not the biggest issue in the world, but in the long run suboptimal sizing add ups to at least some lost EV.
Flop
Against 3 opponents I would also not C-bet, and if CO bets, I would just fold and be done with the hand. Basically treating it as a failed setmine.
Turn
Great turn obviously. There could be some merit to just calling, since it dont look like, either CO or SB has much, and if you raise, you allow them to easily get out of the hand. There is also no flushdraw to charge or protect from. But on the other hand there are straightdraws, and if you call, and someone call behind, BB is likely not going to bluff the river. So all in all I am ok with raising. Basically trying to stack BB and protect against the other players potentially drawing out on you with some random gutshot or whatever. And of course when BB 3-bet jam, its an easy call.