How can I see if a serial number for an apple watch is activation locked?

You cannot. Yes, they removed that tool a while ago.

However, the Serial number is not what is activation locked. What is activation locked is the actual Apple watch. The serial number just identifies the watch but has no lock in and of itself.

Most if not all 3rd party checkers have no way of actually knowing the status of the device in any way shape or form. As there is no public database of activation locked watches and Apple offers no public access to their own.

That really is and has always been the only sure way. Follow the 3 steps in the 'Before you buy a watch from a third-party' section of:

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

You just need to attempt to turn on the Watch. If its activation locked, it will either ask for a passcode, or state that is has been lost or turn on at the home screen. If any of these 3 screens show up, then it has not been correctly unpaired from the paired iPhone and erased.

If its been properly restored and ready for re-sale it will start up to the setup screen.

See here: link-> What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support