You seem to be implying that customer success is a customer support role. It isn't. Customer success is about helping customers get the greatest business value from your product. They are not going to be munging databases and wrangling backups. Support engineers (among others) do that work.

Customers unable to access the product they paid for, for over a week with very little communication, are not experiencing success.

These are the kind of incidents where parties and celebrations are put on hold and everyone does what they can to help, regardless of department or title.

Assuming that the "Global Head of Customer Success" is a leadership role that covers support engineering teams (no clue, but it appears to be some sort of executive position), then it's sorta beside the point whether or not the person is personally munging databases and wrangling backups. If an organization fails it is the fault of its leadership. The buck has to stop somewhere. Whether the "root cause" was risky engineering practices, careless employees, or just back luck, the blame lies with leadership, who should have established safer practices, not hired careless employees, and had a plan to mitigate the unlucky circumstance.

Well right now customers are getting zero value. It’s a bad look to be partying during an all hands on deck emergency.

More hands on that deck probably don't help.

And yet maybe they could have personally responded to the impacted customers with informative, timely updates instead of waiting several days and then sending automated replies from templates.

You’re talking about the outage.

They’re talking about the outage lasting for two weeks without any communication as to what’s going on.