Hello, emensi.
NOTE–Consider making a fresh backup or clone of your Mac on a separate drive before attempting Disk Utility First Aid on your TM drive.
If you can't see the external drive in Finder or Disk Utility, reboot the computer and see if that changes things.
Shut down, unplug your connected devices and restart the computer. Then reconnect the external drive and see where things stand.
If that doesn't fix the issue, please see if the problem still happens in Safe mode.
How to use safe mode on your Mac - Apple Support
Does the problem persist while in Safe mode? If not, then leave safe mode by restarting your Mac normally and re-evaluate the issue again after a normal reboot
Change the drive connecting cable. Does that fix the problem?
If you can get Disk Utility to recognize the drive, then you can run First Aid on the volume and the device.
How to repair a Mac disk with Disk Utility - Apple Support: https://support.apple.com/en-us/HT210898