Portable drive won't mount.

I believe you may be attempting to erase a disk that may be corrupted. You'll want to try to repair the disk before you can do anything else with it. I suggest disconnecting any other external drives before attempting this.

Launch Disk Utility and click View > Show All Devices.

Select the external device named in the sidebar (not any of its contained volumes) and initiate the Erase process by clicking the button in the toolbar.

How to repair a Mac disk with Disk Utility - Apple Support

My practical knowledge of sparse bundles is really limited so I can't much help with this issue. I did grab this link from the web, however: https://eclecticlight.co/2020/04/27/sparse-bundles-what-they-are-and-how-to-work-around-their-bugs/

As for why the external TM backup drive is not showing up in Disk Utility… I'd suggest you reboot your MM in in Safe mode (hold the shift key down at startup). It can take much longer to safe boot (10 min) so be patient. Follow the guidance for the Apple Silicon Mac in this link:

How to use safe mode on your Mac - Apple Support 

Safe mode forces the OS to clear certain caches and logs and do other miscellaneous housekeeping. It's non-destructive to user data so is safe to do. Very often certain weird software behavior is corrected by simply logging in this way as a troubleshooting method. When you're in safe boot, the machine will not be at its best performance, especially with graphics, but that's expected.

Does the problem persist while in Safe mode?

Exit safe mode by restarting your Mac normally and re-evaluate the issue again.

Another suggestion would be to give a disk diagnostic utility app such as Drive DX from Binary Fruit a try. Have it run its tests on the external drive and see if it might find a reason for the problem. I'm still suspicious that corruption is the issue, but you might also consider using a different cable to connect the drive, or even another drive housing if you can manage that for the sake of troubleshooting.

I am having a related problem. I have several external drives (NTFS formatted) that I use for backups and to store photos and videos that I don't need to have on my laptop's drive all the time. These worked just fine with my old MacBook Pro. However, I just upgraded to a newer version and migrated everything over - and now none of these drives will mount. NTFS for Mac can see them, but won't mount except in read-only mode (which doesn't help when I want to back up new material, or move/delete old stuff I no longer need).