#34214 for main (#34271)

Summary:
cherry-pick changes from https://github.com/facebook/react-native/issues/34214 to main. because the `react_native_pods.rb` on main is quite different from 0.69, i have separated pr for the change.

## Changelog

[iOS] [Fixed] - Fix React-bridging headers import not found

Pull Request resolved: https://github.com/facebook/react-native/pull/34271

Test Plan: RNTester + pod install and verify pod targets to have `React-bridging` in header search paths.

Reviewed By: cipolleschi

Differential Revision: D38122074

Pulled By: dmitryrykun

fbshipit-source-id: 64569abbfa3a684f0d6b84c9e3222bfc9a171061