Baptism matters a lot. Salvation comes through faith in Jesus though, which is why the thief on the cross could be promised paradise without ever getting near the water.
When people say ‘baptism doesn’t save’ they usually mean what you guessed, the water itself has no power. Jesus commanded it, and every believer in the New Testament got baptized right after coming to faith, so I wouldn’t call it optional.
I think of it like a wedding ring. Wearing one doesn’t make you married, but refusing to wear one says something about your heart.