I am very sure, that when I last tried Dolby Atmos with the H95 I saw the Dolby Atmos sign on my iPhone. Now, After connecting my iPhone with the H95, the sign disappears when I Start playing the song.So from my understanding, Dolby Atmos (without head tracking) does support all headphones, if I'm not mistaken the device deals with the 3D effect before sending it out as an audio stream. I could be wrong on this additional point, but I do not believe that Apple Music will send out a 5.1 (or whatever surround sound) stream out, but I may be mistaken on that point.
But Apple has been clear that you don't need a pair of AirPods Pro or AirPods Max to listen to Dolby Atmos/Spatial Audio. However, in iOS 15, the support for head tracking Spatial Audio will be implemented and that will require the AirPods Pro or AirPods Max to use. iOS 15 also will do head-tracking stereo too.
Edit: Just forgot to Set it on always on.