Make ui manager proxy not depend on ui manager logic (#52763)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/52763

The ui manager proxy shouldn't depend on the legacy ui manager.

We plan to compile out the legacy ui manager soon. But, the ui manager proxy is supposed to linger around for longer.

Changelog: [internal]

Reviewed By: cipolleschi

Differential Revision: D78697148

fbshipit-source-id: 249c63aae63daf653627e3e449b442b5ddaa5afe