CI/infra/admin improvements - 2024/03 to 05

[chalin]

• [x] #4093
• [x] #4228
• [x] #4234
• [x] #4238
• [x] #4392
• [x] #4437
• [x] #4445
• [x] #4498
• [x] #4564
• [x] #4569
• [x] #4575
• [x] #4583
• [x] #4595
• [x] #4599
• [x] #4612
• [x] #4233
• [ ] #4672
• [ ] #668
• [ ] #2448
• [ ] #2554 - or at least document the currently manual process
• [ ] #2721 - unsure if there's anything left to do
• [ ] #3392
• [ ] #3759
• [ ] #3889
• [ ] #3898
• [ ] #3904
• [ ] #3920
• [ ] #3934
• [ ] #3994

Other:

• https://github.com/open-telemetry/opentelemetry.io/labels/CI%2Finfra in particular see if any of the older issues can be closed.
• #3737
• #3411
• Carried over from #3218:
  • #3117
  • #3183
  • Consider saving the generated website using the artifact action, and passing that along to the link checker