How can I track my Apple Watch with the serial number only

You cannot. The only way to track the device is with Find My. See this, If your Apple Watch is lost or stolen - Apple Support

Hello ~ You cannot. Take a look here:

If your Apple Watch is lost or stolen*

*Find My is the only way that you can track or locate a lost or missing device. If Find My isn't enabled on your watch before it goes missing, there is no other Apple service that can find, track, or otherwise flag your device for you.

~Katana-San~