When I said "probably a fairly rare one", I didn't mean that the outages are rare. I meant that new code is probably a rare cause of the outages that happen. They have other causes unrelated to new code.
(I'm also skeptical that GitHub major outages happen "nearly weekly", but I don't have data.)
It's a startup site with half the people not having a test environment.
The above was sarcasm.
If your org has CD and it does not have CI validation step that provides 100% test coverage of your code, then you do not have a CD - you have MSP - Merge->Ship->Pray system in place.
What one should do is push the new feature dark, i.e. not enabled for anyone except the automated test suite user. That's the user that should exercise all old paths and validate that no old path is broken when the feature is enabled by a user but unused. After that is validated in production one can enable the feature for either a percentage or users or 100% of users depending of how one is playing to live test and live QA the feature.
The important part is that no new release can break existing usage patterns.
That's CI/CD. Everything else is magic, unicorns and rainbows.