Stockfish isn't convinced that f4 Be7; f5 Bd7 does give W a comfortable advantage; it reckons +0.2, same as if B plays ... Be7 after Nb3 as you recommend. Again, I'm a patzer so if your intuition/calculation says W is much better I don't have any refutation other than "computer says no". W's position sure looks more fun to play, with prospects of a kingside attack, but that's often true in the Sicilian even when things are objectively fairly balanced.
If I let it sit for a while, it vacillates between wanting to play g4, a3, Be3, h4, etc., and a quieter approach with Bg5xf6, Qd3, Nd2. At depth 46 it prefers the latter but only gives it +0.1 even though its PV shows W winning the d-pawn. Aaaand at depth 48 it's switched back to Operation Pawn Storm, though it wants to prepare with a3 and Bf3 before playing g4 and h4. And back to the piece manoeuvres and winning the d-pawn at depth 50. Still only +0.1, though.
(But computers are awfully good defenders, and maybe this is one of those positions that's much better for the attacking side when humans rather than computers are playing.)
Black here has very natural development - his bishop is controlling d5, his knight is ready to jump to d4 (thus interfering with white heavy pieces control of d-file). Because of this he can liquidate into drawn (if difficult due to worse pawn structure) ending after 11. O-O-O Nd4 12. Nxd4 exd4 13. Nd5 Bxd5 14. exd5
This way of playing with Bg5 is not so popular anymore today (Be3 is way more topical, with either O-O or O-O-O), but it offers clearest comparison to analogous position.
Black needs to control d5 and e6 is off-limits, so he has to reroute his bishop to c6, where his knight wants to be. White has lasting pressure on d-file, it's not clear how black will develop his knight and he cannot easily force pieces off the board.
If I let it sit for a while, it vacillates between wanting to play g4, a3, Be3, h4, etc., and a quieter approach with Bg5xf6, Qd3, Nd2. At depth 46 it prefers the latter but only gives it +0.1 even though its PV shows W winning the d-pawn. Aaaand at depth 48 it's switched back to Operation Pawn Storm, though it wants to prepare with a3 and Bf3 before playing g4 and h4. And back to the piece manoeuvres and winning the d-pawn at depth 50. Still only +0.1, though.
(But computers are awfully good defenders, and maybe this is one of those positions that's much better for the attacking side when humans rather than computers are playing.)