Mounting or unmounting a filesystem won't make a difference for drive longevity.
If you want to keep your backups secure, you want to keep them offline, so if you get ransomware it doesn't encrypt your backup too. (Or if you just mistype a command and target the wrong device, folder, etc.)
But drive motor starts and stops are when the most failures occur. So the ultimate question isn't how to make a drive last longer, it's how you plan to handle it when the failure inevitably occurs.