What if you forgot your old Apple ID password for your Apple Watch

You will need to recover the old Apple ID or the watch will consider itself as lost or stolen and remain under Activation Lock to the old Apple ID.

https://iforgot.apple.com/password/verify/appleid

M1 Mac mini, macOS 11.3; Watch, series 5 GPS/cellular, watchOS 7.4; iPad Pro 2nd Gen, iPadOS 14.5; iPad Air 2, iPadOS 14.5; iPhone 12 Pro, iOS 14.5; TV 4th Gen, tvOS 14.5  HomePods, audioOS 14.5 and Airport Express w/ Airplay 2

Request an Online Activation Lock Removal here.

Or this;

If you can't remember/gain access to the apple id that paired the watch to the phone.Take the watch and it's receipt along with some photo id and any other proof of ownership to an Apple Store and request that they remove the Activation Lock for you.

Otherwise the watch will be of no use to you.