Update contact channels

[The-Compiler]

Follow-up to #12427 plus some more cleanups:

• Mention core@pytest.org as mail point of contact (not live yet, hence why this is a draft PR)
• Also add a list of core maintainers receiving such mails. Unfortunately the GitHub Team page is not public, so we can't just link to it. Still I feel like it's important to have a public-facing list of people that actually are in the core team, and I suppose this will be the right place?
• Mention Bruhin Software for trainings/consulting. Let me know if you'd rather not have me do that, but given that Merlinux was mentioned there and I pretty much took those things over from Holger, I suppose it should be fine?
• Remove dead link references
• Restructure channels into different groups for more readability
• Fix broken links from Update contact.rst: Update Matrix link #12455
• Other minor edits

[The-Compiler]

Preview: Contact channels - pytest documentation

[The-Compiler]

Sorry for the push spam, I missed that #12455 broke various links when rebasing 😅

All ready now, and the mails are live too!

[patchback]

Backport to 8.2.x: 💚 backport PR created

✅ Backport PR branch: patchback/backports/8.2.x/423f71963c9a4b6a06d8322407d6cef05184c9a2/pr-12515

Backported as #12603

🤖 @patchback
I'm built with octomachinery and
my source is open — https://github.com/sanitizers/patchback-github-app.

[nicoddemus]

Thanks @The-Compiler!