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.
It wont once you transfer from Iphone to Iphone, I Just got the Iphone 15 and I am still on watchOS 9 no update needed for the watch.