Restoring external boot drive with Time Machine?

I’ve been running Mac OS 14.1.2 off an external hard drive (SAMSUNG T7 Shield 4TB SSD, 2.5ish TB in use, APFS GUID Partition Map) from my Mac Mini 2018 Intel core thingy, and backing the external drive up with time machine.

The drive failed to boot up today (system restart cycle: computer freezes at startup disk password screen after I enter my password; eventually restarts and sends me back there), so I decided to jump back into my internal storage (256GB SSD) and use disk utility or time machine to reset and restore the external drive. First aid unfortunately did not work as far as I tested 😓

How would I restore my external boot drive correctly with a time machine snapshot?

The option to restore is grayed out when I enter time machine. Recovery mode is only letting me restore the internal storage. I could erase my current time machine drive/spring for another extHDD and use Carbon Copy Cloner to make an additional backup of the drive’s files, or make a new disk image???

What are my options here?