Moving beyond stereo, like Amazon Music and Apple Music are, is definitely emerging, but in the case of those two companies their target markets appear to be smart speakers (Echo & HomePod). Yuck.
Apple's target is spatial audio with their own headphones. AppleTVs will also play the Atmos music direct to your AVR or whatever, it works well. It's actually the best source of streaming multi-channel music out there.
You don't really need special headphones -- what you do need is some way to do head tracking. There are various approaches including some that use webcams etc. But obviously the best usability is headphones with that hardware built-in like the Apple ones.
Amazon sucks at music or really any media lol, Prime Video is terrible too.
I can only tell you what I've been told by a manager at UMG, which is that they're strongly encouraging all their artists to opt in to Atmos versions of their albums if they're even remotely popular. I'm sure it's not universal but there is a strong drive at some of the biggest labels.I'm not convinced that multi-channel headphones are driving the recording industry in any way.