Wear Screenshots Saver shows up as share target. Once you choose to share screenshot from Wear OS device with the app, it will save it in public Screenshot folder (where screenshots made on the phone are saved).

This is fork of the app with the same name made by KiyohitoNara. I've rewritten app in Kotlin and added support for runtime permissions or invoking media scan after saving a screenshot, so gallery apps can see it right away.