How can. Unlock my Apple Watch if I forget my old Apple ID

The Apple Account (Apple ID) that has been used to pair the Apple Watch will be shown during the paring process:

Set up your Apple Watch - Apple Support

But you also check other devices, to find the used Apple Account:

If you forgot your Apple Account primary email address or phone number - Apple Support

If this does not work and you have proof of ownership, the official Appel Support can disable the Activation Lock:

Additional Support - Activation Lock