How do I remove Activation Lock from second-hand Apple Watch with proof of purchase?

You may wish to start with this link:

 https://al-support.apple.com/#/getsupport

There is a link to start an Activation Lock support request:

https://al-support.apple.com/#/al/agreement

If the “Still Registered w/ Apple” owner is reluctant to disclose their password (and they should be unwilling to do so) …

… they can release the activation lock remotely as described here:

How to remove Activation Lock - Apple Support

Be prepared … unless that “official” proof of purchase is documenting the “original purchase” — i.e. from Apple or an Apple-authorized reseller — your prospects for success in unlocking are likely diminished.

Best of luck regardless. 🤞

In this situation, a receipt documenting a subsequent “private resale” might not be worth any more than the paper on which it’s printed.

You would have to contact the original owner. Or ask the seller to give you contact information for the original owner. They should either provide you with their original receipt (that has the serial number), or better yet, provide you with the password to unlock that watch. Here is what the original owner should have done:

What to do before you sell, give away or trade in your Apple Watch, or buy one from someone else – Apple Support

This article offers good advice to consider before purchasing a used Apple device.

The All Too Common SAD Reality of Buying … - Apple Community

You don't. Return it and get your money back if you can.