To add to the speculation. The error messages we were observing along with the Microsoft status updates read like connection pool exhaustion. The ticket update history started with Microsoft thinking a 'restart of affected servers' fixed it and troubleshooting 'health check failures'.

Anyone who has seen connection leaks/pool exhaustion in practice, it looks like an otherwise healthy low utilization server right up until it stops replying, and a restart appears to fix it until it runs into the limit again. Easy to think that your health checks are the problem. Per MS updates, they rabbit holed on this issue and built 'an alternative health check method' which worked in testing (i.e. low number of test connections); but when they tried to apply this change, servers would go unresponsive anyway.

My guess is a rushed update with a connection leak somewhere in the stack. A call that opens, but does not close. Just the kind of thing that AI can miss because it's only trying to hit the goal and not necessarily clean up after itself.