I do this with my WearOS smartwatch (gen 4 Fossil Sport). It works pretty well overall, although I had to find a third-party app (WMusic) to allow copying music to the watch and playing without an active connection to the phone.
I just got an Apple Watch, and am planning to experiment using it without the phone.
It has WiFi but no cell phone. Really looking forward to just being out for runs, with no possibility of contact or checking notifications etc.