If your watch was set-up with an old Apple ID and you now have a new Apple ID, you will have to recover the old Apple ID to release the Activation Lock on the watch to the old ID. Activation Lock prevents lost and stolen watches from being used by others. It can't be defeated.
Activation Lock removal -
How to remove Activation Lock - Apple Support
https://al-support.apple.com/#/additional-support
Call and speak directly to Apple Support for help recovering the use of your old Apple ID.
World-wide Apple Support -
Contact Apple for support and service – Apple Support
Alternatively, take the watch, the original purchase receipt for the watch with the watch's serial number and your personal ID to an Apple Genius Bar for help removing the Activation Lock. You need to make a Genius Bar appointment before going to an Apple retail location.
Genius Bar Reservation and Apple Support Options - Apple
M1 Mac mini, macOS 13.5.1; Watch, series 7 GPS/cellular, watchOS 9.6.1; iPad Pro 2nd Gen, iPadOS 16.6; iPhone 12 Pro, iOS 16.6; TV 4th Gen, tvOS 16.6; HomePods, audioOS 16.5 and Airport Express w/ Airplay 2