As someone who worked in infrastructure for a large global CDN, this sort of overload issues happen all the time when trying to bring infrastructure back online after an issue.

First, you have every client retrying connections, whether automated or manual retries. This generates extra load over normal.

In addition, whichever systems come online first often get a ton of traffic sent to them, which can immediately bring them back down if you don't have ways to prevent it. You will get a wave of systems coming back online, a ton of traffic hitting them, and then falling over again.

Now, I am sure Microsoft is used to this and has procedures and systems in place to mitigate the issues (I know we did).

However, sometimes if the right combination of services are failing, even the strategies you had to avoid this sort of failure can themselves fail.