backing up external hard drive and MacBook Pro hard drive
How do you back up the ScanDisk Extreme Pro external drive on the Seagate Portable Drive if its grayed out on Time Machine?
MacBook Pro 16″, macOS 14.1
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Time machine backs up every Mac formatted drive connected to your computer. it can not back up drives that are not inherently Mac formatted.
based on the number for trademarked names you tossed out in describing your drive, my bet is that you did not ERASE that drive back to bare metal with Disk Utility when it was new and blank, but just loaded the drive-maker's utilities, and allowed that drive to stay controlled by their drivers.
The additional downside, besides that you can't back it up with time machine, is that if those third-party drivers are not loaded, such as after a disaster on in recovery mode, the drive may be inaccessible.
The standard advice given here to all users, including novice users, is to discard the manufacturers software and NEVER use it. "Best Practice" is to erase the physical device when new, using only MacOS Disk Utility, and create the fundamental Volume data structures needed for consistent, reliable use by MacOS.