If your Apple Watch needs to have the battery replaced, and your watch is covered by Apple Care or you pay the service fee, Apple will replace the whole unit, not only the battery.
In case the watch is not manufactured anymore, Apple can not provide this service no longer.
...
Owners of iPhone, iPad, iPod, Mac, Apple TV, Apple Watch, AirPods, Apple Vision Pro, and Beats products may obtain service and parts from Apple service providers for a minimum of 5 years1 from when Apple last distributed the product for sale.
Service and parts may be obtained for longer, as required by law or for up to 7 years1, subject to parts availability. Additionally, Mac laptops may be eligible for an extended battery-only repair period for up to 10 years from when the product was last distributed for sale, subject to parts availability.
Apple discontinues hardware service for certain technologically-obsolete products. Your product is supported by ongoing OS updates and backed by a network of more than 5,000 Apple-certified repair locations that you can count on if something unexpected happens.
...
copied from: Obtaining service for your Apple product after an expired warranty - Apple Support