os x base system

The SSD appears to be dead. If so, it needs to be replaced, and any data on it can only be recovered by a professional service.

(161430)

Did you install it in an external enclosure, adapter, or "toaster"-style adapter first?

Did you replace the drive cable in the name of routine maintenance?

MacOS Base system is a bootable Installer image, about 5+GB in size.

it must be stored somewhere, so your drive may not be dead, just damaged.

¿So is this a safe statement? :

"After a Bad Startup that dumps you into Internet Recovery, if your Boot Drive is absent from Disk Utility, the MacOS Base System you see is likely to be the one potentially available on Apple's Servers, and is not likely to be a local copy on your Mac?"

Or is there a more precise way to describe that situation?

OtherWorldComputing/MacSales is very Mac-centic company that prides itself on their great customer support -- both Sales support and Technical support.

They don't carry anything that is troublesome, because it would give them support nightmares. They have developed or sponsored many exclusive products for the Mac, and are trying to continue to do so.

It's stored on Apple's servers.

(161468)

When you see it in Disk Utility, Is that a copy locally on your Mac, or a copy on Apple's servers?

It's on Apple's servers.

(161470)

Only in Internet Recovery, or always?

For Internet Recovery, but if someone reinstalls the OS from the recovery partition, it gets redownloaded.

(161472)

If a physical drive doesn't appear in the Disk Utility, the computer isn't seeing it, and won't be able to load anything from it.

(161474)

Then those are the things that will tell you whether the drive is dead or the cable is dead, or it's something else.