I found an Apple Watch, how do I find the owner?

I’d like to keep it if the owner doesn’t want it back.

As stated Apple won't help you find the owner.

Additionally, the watch is currently on Activation Lock. It is locked to the owner's Apple ID to prevent lost and stolen watches from being used by others. If the owner doesn't release the watch, you can't use it.

M1 Mac mini, macOS 14;  Watch, series 7 GPS/cellular, watchOS 10.0.1; iPad Pro 2nd Gen, iPadOS 17.0.3; iPhone 12 Pro, iOS 17.0.3; TV 4th Gen, tvOS 17; HomePods, audioOS 17 and Airport Express w/ Airplay 2

You don’t, and Apple won’t assist you. Take the watch to the local police department and let them handle it. As for keeping it you can’t do that either as it is Activation Locked to the original owner and would require cooperation from the original owner to use it. Sorry, it’s all about security and privacy.