Act as @react-native-bot on all the actions (#45480)

Summary:
Pull Request resolved: https://github.com/facebook/react-native/pull/45480

We currently use the default GITHUB_ACTION which makes a lot of interaction
appear as user "GitHub Actions". Instead we could use the `REACT_NATIVE_BOT_GITHUB_TOKEN`
which we have as secret so the bot will actually perform the actions.

Changelog:
[Internal] [Changed] - Act as react-native-bot on all the actions

Reviewed By: cipolleschi

Differential Revision: D59815201

fbshipit-source-id: 702b121ec07d0db10abf25e23f7ddf5658dd5d62