sync-react: Remove redundant work in

This mainly moves code out of the `sync` function into a parent main function.
The `main` takes care of the responsibilities that we really only need once while `sync` takes care of just syncing this specific React release channel:
- update peer dependencies
- install
- compile
- print changelog

The changelog could live in the `sync` function since it's technically specific to each release channel.
However, currently don't write React commits to indicate which release channel they affect.