RANDOM SHUT DOWNS ....HELP!!!! MacOS needs to be reinstalled? Startup disk or recovery key???

'Recovery- KEY' is NOT the same as Recovery. Recovery-KEY which is used when your Mac is lost and you remotely lock it. The recorded (on paper) Recovery-KEY is used to unlock it when found.

Recovery is the minimal macOS (built into modern Macs) that supports one-at-a-time operation of Utilities like Disk Utility and Installer, and can help you re-download and re-install MacOS.

is the battery fully charged?

Please connect the charger and get the battery more fully charged, if so equipped. Recovery will require the power adapter be connected to make substantial progress.

¿what model and model-year is this Mac?

the version of macOs needs to be re-installed. you use recovery to do that, and it requires your admin password to do anything.

You have a modern Apple-silicon M1 Mac, and running Sonoma (slightly older than latest version).

So if you want to use your computer, connect the power adapter, choose (Recovery) or choose Command-R at startup, enter your Admin password ,and re-install MacOS, just as instructed.

By design, a re-install of same version of MacOS does not disturb User files or User-added Applications. But over 350,00 system files will be re-written.

when possible, it is prudent to have on hand a trusted backup of all your files in case something goes wrong. when your Mac is working again, that should be a top priority. obtain an external drive at least as large as what you need to save (preferably 2 to 3 times as large) and use the built-in Time machine to make you a backup automatically. "It just works."

In your first screenshot, the choices are

• (Recovery) enter Recovery mode to check the disk and get it working

• (Startup Disk) use your OTHER, already setup external disk drive with a different MacOS already installed on it.

You probably don't have that, so that is NOT a viable option for you.

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if your issue is related to sleeping, there are settings that can be changed so that it does not sleep automatically:

Set sleep and wake settings for your Mac – Apple Support (AU)

make them all not sleeping until you figure this out.

[Edited by Moderator]