RN: Update `set-versions` for `private/` Packages (#51937)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/51937

Updates the `set-versions` script to also update workspace packages in `private/*`. Unlike with packages in `packages/*`, this does not change their `"version"` fields, though. It only updates their dependencies.

Changelog:
[Internal]

Reviewed By: huntie

Differential Revision: D76358273

fbshipit-source-id: d0e0557d17c355828020a218083b98dd177a6732