Remove ReactFabricPublicInstance and used definition from ReactNativePrivateInterface (#26437)

## Summary

Now that React Native owns the definition for public instances in Fabric
and ReactNativePrivateInterface provides the methods to create instances
and access private fields (see
https://github.com/facebook/react-native/pull/36570), we can remove the
definitions from React.

After this PR, React Native public instances will be opaque types for
React and it will only handle their creation but not their definition.
This will make RN similar to DOM in how public instances are handled.

This is a new version of #26418 which was closed without merging.

## How did you test this change?

* Existing tests.
* Manually synced the changes in this PR to React Native and tested it
end to end in Meta's infra.