I think it's a very interesting topic! I would also welcome more communication to and about new contributors.
About people getting commit privileges, it's not really happening a lot these days. I have mostly stopped proactively inviting people to the organization after seeing them send a couple of successful PRs, because it's not following any sort of process. I have been thinking about a better system, and proposed a rough draft here:
About people getting their first pull request in, the "first-time contributor" badge that GitHub displays on pull requests is helpful to me, but it doesn't do the tooting on Mastodon by itself 
I'd intuitively welcome some sort of automation or written process to ease things, so that we don't leave too much of it up to the person who merges the PR.
I think there are also tools to list the first-time contributors in the changelog of a release, we could also look into adopting that.