Introductions under General seem fine to me. If it ends up not working, it’s very easy to move topics.
As far as workflow, I find Discourse works really well for asynchronous, long-form communication that you need to be discoverable (so basically the opposite of Slack).
If it’s mostly developers taking about filed issues that are closable with a pull request, then GitHub is adequate, but if you expect non-devs to participate and it’s not about issues, then GitHub is a bit too much. I bias to starting conversations on Discourse and once it gets to something closable with a PR, filing it as an issue on GitHub.
Final thing to know is that you can probably get rid of Google Groups. That is, you can flow emails in and out of Discourse relatively easily for one-of conversations. The caveat there is if you want something that’s more for one-way announcements, then Google Groups is hard to beat, but I’d probably use Mailchimp or something similar.