So what pool session does PADI introduce neutral buoyancy?
Module 1. I may be a bit of an enigma, but I not only introduce neutral swimming in module 1, I introduce hovering too.
We (all of the instructors at the shop where I work) spend a LOT of time on neutral swimming throughout the course. During Mod-1 what I do is get the students moving and then lead them to the deep end of the pool while moving slower and slower until I'm not moving at all. At this point they also stop moving and are essentially hovering.
I discovered this by accident years ago and it was one of the triggers that put me on this journey of learning to teach the entire OW course while neutrally buoyant.
I realized that almost anyone can hover (to some extent -- obviously it's not perfect yet) straight out of the gate if you introduce it like this and are very directive about when they need to put air into the BCD or let it out. I don't brief hovering as a "skill" ahead of time in mod-1 but I do set expectations before going to the pool and I debrief it, explaining that this "floating" thing they did is what I want them to do as much as possible. I then instruct them that at any time during the training when they need to "wait" for any reason, they need to "wait" while hovering (or at least trying to hover).
All of this happens in module-1.
R..