> How likely is Valve to use Android?

Not likely, unless they make a headset which doesn't do much of anything by itself and is just meant for streaming from a PC. To make a standalone headset which can draw on the Steam catalog they would almost certainly want to use a variant of their SteamOS Linux distro.

Valve already has its own OS for a mobile device: Steam OS (based on Arch) on the Steam Deck. My bet is that they'd just modify that for a standalone headset.