Just got the new Iphone 15 and was able to stay on Watch OS9 using “transfer from Iphone to Iphone” It does not update the watch. I do believe if you restore from Icloud or factory reset you have to update the watch because it has to be re-paired. Just thought I’d let anyone no who is hesitant to upgrade, that it is possible to stay on Watch OS9.
As long as your WatchOS version is supported by your iOS version, you don’t need to upgrade even if you unpair and re-pair the watch