refactor: emit the trace recoding on ReactNativeApplication domain initialization (#53760)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/53760

# Changelog: [Internal]

This is a different approach from the one that I've introduced initially in [1].

This saves us from the scenario, where any local session could snatch the stashed trace recording. For example, if some session was created for a Runtime binding right after we've stashed the trace and before initializing real CDP session with the Frontend.

Reviewed By: huntie

Differential Revision: D82316584

fbshipit-source-id: 806a0f6dbdb4e4e928ce33af228cae86d43772e9