Just throwing in my lot. Tried everything in this thread.
Same for me - holding Windows and hitting play/pause causes Spotify to pause/play at least. But otherwise only the previous/next track media keys work - it's the same whether it's on my keyboard or my mouse assignments. Even with no other apps open (including in the background).
Hilariously, when I was on Windows 10, I had the opposite problem - play/pause would work, but not skip. New PC now, on Windows 11, and it's just hilarious that it's the same problem, but inverted.
Really hope a solution comes down the pipeline. I use media keys *constantly*.