I have been running my Pixel watch on my Fold, and I'm waiting for PW3 to connect to my P9PF. That being said, please don't pretend like you are maintaining any level of privacy if you do this. Even if you somehow ran the watch without your GoS phone and attached it to a junk phone in a drawer just to relay notifications, you're still giving just about everything to Google.
I'm about 60% complete with my de-googling operation, which has taken 4+ years, and when I get closer to the end, there's no way I can justify having a Google watch. It makes GoS nearly pointless. I consider what I'm doing now as more of a learning experience. What works, what doesn't. I'd kill for a GOOD Linux watch. I do use a TicWatch Pro 3 GPS with limited app connectivity as well, since it's so good at sleep monitoring with SleepAsAndroid, but I'm sure there's some leakage there as well.
At this point, I think I'd rather China steal my data than Google/The US Government.