external hard drive mounting issue

What's your particular setup? Drive, maybe enclosure, and what kind of cables/hubs/adapters are you using? What format(s) for the drive volume(s).

At the very least I would suggest looking in System Report - > About This Mac - click on "System Report" and then look under Hardware > USB and see if it shows up in the USB tree somewhere.

Other than that, open up Applications > Utilities > Disk Utility and see how it shows up. Often that will show a drive that is present but not mounted.

Make sure to connect the drive directly to the laptop to eliminate compatibility issues with adapters, docks, and hubs. Also try connecting the drive to another USB port especially on the other side of the laptop if possible.

Keep in mind some third party devices may not be compatible with an M1 Mac. I have seen numerous reports on these forums as well as having a experienced this first hand with one of my devices.

Also, macOS 12.x Monterey introduces its own compatibility issues with some devices and the proprietary third party software some people use to manage their external drives especially those using the NTFS file system.

Try restarting the laptop and try booting into Safe Mode to see if either one makes any difference.

Are you using any anti-virus apps, cleaning apps, or third party security software? If so, then that may be the source of the problem as these types of apps interfere with the normal operation of macOS.