cannot find cost to buy applecare for my watch without serial number input. How can I find out?

You will need to ask Apple - we are all other users here and, unless Apple has published the information, we have no access to those records. Most likely, the price depends on the country/region and model.

https://www.apple.com/support/products/watch/

You can probably find out if you do a chat at the online Apple store.