I just wanted to make this PSA for anyone who may have had the same problem as me and can find this via a google search.
I had a series 3 issue a week ago. I disconnected it in an attempt to resolve the issue, but after pairing I always got an error saying I need to install the latest iOS (14) to connect the Apple Watch.
It sat on my desk for a week until I charged it and messed with it again. When I used the “pair manually with code” option instead of using automatic pairing, I was shocked when it allowed me to restore my last backup!
So yeah just wanted to throw this out there. Good luck everybody