Weirdly enough, Bitwarden does support Watch unlock already, but only when using biometry to unlock a browser plugin! To clarify, the browser-to-desktop-app authentication seems to accept “any biometric identifier” while the desktop app authentication itself only accepts Touch ID.
This is probably because the unlocking key is stored in the macOS keychain with a requirement for Touch ID to access, while the browser unlock request only works with the desktop app already unlocked. In this state, the desktop app does not need to unlock anything, but just needs to ask macOS to authenticate the user and then hand over the corresponding key from memory.
It would definitely be cool to have Watch unlock in the desktop app itself – as it is, I have to enter my password in the desktop app in order to be able to unlock my browser with the Watch.