Go to icloud.com and login
Open Find iPhone.
In the All Devices pulldown menu select your Watch.
In the resulting sheet that appears to the right choose erase Apple Watch. Select Next until the device is erased.*
Then Remove the watch from your Apple ID.
*You are going through the motions so that you can get to remove the watch from your Apple ID.
M1 Mac mini, macOS 12.6; Watch, series 5 GPS/cellular, watchOS 9; iPad Pro 2nd Gen, iPadOS 15.6; iPhone 12 Pro, iOS 16; TV 4th Gen, tvOS 16; HomePods, audioOS 16 and Airport Express w/ Airplay 2