The way forward is to generate a new CA root certificate.
> and they can no longer run puppet because the puppet master's CA cert expired
They can reconfigure internal tools to use the new CA root certificate, or rather one of the signed intermediate certificates.
> and they can't get a new one because no one has access.
They can simply generate new CA root certificates, and sign or create new intermediate certificates.
> They no longer can mint certs.
Yes, they, can...
> My limited understanding in this area is that this is...very bad
No, it, is, not...
There are two immediate issues that come to mind.
* Twitter was so awful before, that it relied on people to safeguard the keys to the kingdom. This is very bad practice, and one of the many things Musk will no doubt be fixing. For any mission critical assets, and especially certificates, but also passwords... current modern day corporate practice is to have a secure ledger of these that can be accessed by the board of directors, the executive managers, and designated maintainers. At no point ever should the password be entrusted to anybody, but rather a "role" that functions as the one who has access. Say for example, the CIO/CTO and their subordinates.
* The Second issue is the one everyone is fixating upon, and that's firing important people who put the company at risk. This is a big issue, and certainly Musk could have done a better job of scoping out who represents a single-point-of- failure at twitter, eliminate that risk, and then proceed with the culling. In a modern enterprise no single person should be capable of putting the entire operation at risk. It's just that simple. So in a way, Musk accelerated what was probably inevitable at Twitter already. They were probably precariously close to destruction already, and now they can learn the hard way of not repeating these mistakes.