feat: Add Running... note to the init command

[cortinico]

Summary:

This is an implementation part of react-native-community/discussions-and-proposals#759
I'm waiting for the RFC to be approved before we can merge this, but I'd like to get a review.

Test Plan:

@szymonrybczak do you know how I can easily test this?

Checklist

• Documentation is up to date to reflect these changes.
• Follows commit message convention described in CONTRIBUTING.md

[thymikee]

You can check our e2e tests under __e2e__/init.test.ts. Some will likely fail because this will be logged in the text stream written to snapshots

[cortinico]

You can check our e2e tests under __e2e__/init.test.ts. Some will likely fail because this will be logged in the text stream written to snapshots

Great will wait for test failures to follow up here then

[cortinico]

Closing in favor of facebook/react-native#43127