The answer that worked for me is what drmwho noted above:
<quote>
I found some suggestions on the LaCie support site.
Some Seagate and LaCie software use a kernel extension (kext). Apple
silicon Macs require that users change the security settings to ‘Reduced
Security’ for the software to function properly.
To change the level of security on your startup disk:
Shut down the Mac
Press and hold the power button until you see “Loading startup options”
Click Options
Click Continue
If asked, select a user > Click Next > Enter password for admin account
In the menu bar at the top, Select Utilities > Startup Security Utility
Select the startup disk
If the disk is encrypted, Click Unlock > Enter Password > Click Unlock
Click Security Policy
Select Reduced Security
Put a check next to “Allow user management of kernel extensions from identified developers”
Click OK
Enter admin password > click OK
Once changes are applied, click the Apple icon and Restart
Once you adjust startup security, restart and reconnect the drive, it should work. It has to do with letting the drive's software install a kext so it can mount, as I understand it.
Good Luck! I struggled and cursed Apple's lack of info on this, finally succeeded.
I also found Glenn Fleishman's "Take Control of Your M-Series Mac" very helpful, although he does not specifically address this as a fix for hard drives not mounting. His section on the startup security settings gave me confidence that this was a real, safe thing to do (not just a drive manufacturer hack). Lots of other great M1 info also.
Once I did this, the drive mounted and showed up in Disk Utility, which it would not do before. Hooray!