Remove the "Newer Patch Available" logic from @react-native-bot (#51286)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/51286

This bog action is not really useful. It's currently buggy and spams the user twice + we agreed it provide little value for the user.
Therefore we're removing this message for the time being.

Changelog:
[Internal] [Changed] -

Reviewed By: cipolleschi

Differential Revision: D74645716

fbshipit-source-id: a6b8aa6aa3f3f101ad649d2590bbcb2dc80ee30a