I also hit this issue trying to set up a service replacement from Apple. I spent hours trying all these suggestions on my main iPhone 11 without success. I even set up an old iPhone 8 from scratch (as a new phone, but still linked to my iCloud account) and that still failed in the same way.
The solution for me was to set the watch up using my wife’s iPhone and iCloud account first - the update went through first time. I then removed it from her account and was then able to set it up successfully on my phone and iCloud account, as it didn’t need to do the update, so didn’t hit this error.
So, for me at least, it seems to be some sort of issue with my iCloud account (or some data synced to it), possibly related to the way the Genius removed my old watch from my account when I took it in for servicing.