One click, zero data corruption
Install SeventyEject, plug in your external drives as usual, then click the big « Eject all » button (or use the menu bar icon). Every drive is cleanly unmounted, in sequence, and a checkmark confirms success. If a drive resists, the app says so clearly instead of failing silently: "macOS is holding this drive back (file still open?)".
Download the free SeventyEject trial (7 days, macOS 13+).
The most common message is "macOS is holding this drive back": a file, document, or Finder window is still using that volume. Close the apps involved, check that no Time Machine backup is running, then try again. As a last resort, macOS's Disk Utility offers a forced unmount.
SeventyEject ejects any external volume macOS recognizes as removable or ejectable, including Time Machine backup disks. The one case to avoid: ejecting mid-backup, macOS will warn you if that's happening.
Get SeventyEject: 7-day trial, then a lifetime license.