[tool] Restore publishability (#11745)

Restores the repo tooling to a publishable state, so that we can start using it for flutter/core-packages.

I expect fixes will be necessary to make it actually work correctly in that repo, but this gives us a foundation to iterate from where we can actually publish and test changes:
- Removes `publish_to: none`
- Restores the old CHANGELOG, and adds a new entry for the new version.
- Moves the formatter download cache to the repo root instead of a directory that other repo's wont have
- Changes the setup to find the repo root by walking up from the current directory until finding something that looks like the repo root, rather than hard-coding a relative path from the invoked script.
- Adds back some initial documentation about how to use this in another repo. Having two ways of running it was always confusing to explain, so this tries a new approach of demonstrating setting up an alias, and then having all the examples use that alias. We may need to iterate if that proves confusing (to people and/or to AI agents)

Fixes https://github.com/flutter/flutter/issues/185764