yes, it’s all those things. mostly it’s his own personal thing which is embouchure and air control. personal choices with reeds and mouthpieces of course will contribute by allowing the player to do what they want to do. as for that beautiful breathy sound my favorite is Ben Webster, I put up a blog post on him a little while ago where you can give a listen to this: https://howtoplaysaxophone.org/ben-webster
.
.