I have a similar issue, but I don't think that "Monterey struggling with External SSD" should be marked as "solved" because the proposed solution requires a specific hardware configuration. A general solution is needed. Here is my experience.
I have a MacBook Pro (13-inch, 2020, Intel processor) and two portable Samsung SSD's. One is the X5 with a Thunderbolt interface, and the other is the T7 with a USB interface. I use the X5 for Time Machine backups and the T7 for general purpose storage. I started with macOS Catalina and later upgraded to Big Sur. Everything worked great. The X5 is so fast that I seldom notice that backups even happen. Then I upgraded to Monterey (currently patched to 12.2.1) and started having issues with the X5.
Before Monterey, I could unmount the X5 and T7 and then unplug them. No problems. Now with Monterey, when I unmount and unplug the X5, it seems to work, but later when I plug it back in, it won't mount. Instead, it just gets hot, like it's working hard on something but unable to complete it. To recover, I need to shut down and restart the MacBook. Then I can plug the X5 in and it will mount normally. This is not an acceptable workaround.
First, I tried to update the Samsung software, thinking that maybe my older version was incompatible with Monterey. I carefully followed Samsung's Troubleshooting Guide for macOS (Revision 1.1, 2021). None of the advice in that document solved the issue. Next, I reformatted the X5 from Mac OS Extended to APFS. (Yes, this erased all my backups, but I was willing to pay that price.) That didn't solve the issue either.
Then I tried a few things in an attempt to isolate the problem or at least find some clues. Using Disk Utility, I can mount and unmount the X5 and T7. I can do this multiple times with no issues, and I can see the mount point appear and disappear in Disk Utility, Finder and Terminal. Again with Disk Utility, I can eject the T7 but not the X5. When I attempt to first unmount and then eject the X5, I get the error message: "Failed to eject Samsung Portable SSD X5 Media because it is currently in use." What could be using an unmounted volume? It must be some component of the OS, maybe the Samsung driver or something in Monterey (Spotlight? Time Machine?).
Next I used Disk Utility/First Aid. Running it on the APFS volume I got the following message:
Checking file system and repairing if necessary and if possible.
Volume was successfully unmounted.
Performing fsck_apfs -y -x /dev/rdisk3s2
error: container /dev/rdisk3 is mounted.
File system check exit code is 65.
Restoring the original state found as mounted.
File system verify or repair failed. : (-69845)
Next I unmounted the APFS volume and ran First Aid on the APFS container and got the exact same message as above.
This is consistent with the behavior I found when trying to unmount and eject the X5 using Disk Utility. What does it mean that the volume is unmounted while the container is mounted? When I unmount the volume, there is no option to then unmount the container. I don't understand what's going on here.
Finally, I unmounted the APFS volume and ran First Aid on the X5 media. That ran successfully with no errors.
After this, I got the idea of unmounting the X5 and leaving it plugged in while closing the MacBook lid. I waited half a minute for the computer to fall asleep and then unplugged the X5. Maybe the sleeping OS wouldn't notice me unplugging the X5. Starting up again, I reversed the sequence: plug in X5, open lid, mount X5. To my amazement, this worked! Except that I didn't need to perform the last step: when the computer woke up, the drive was already mounted. This is an OK workaround, though it's not great because now I have to carry the X5 with me all the time.
Best would be an OS that worked as well as before. The X5 worked just fine with Catalina and Big Sur, which points to Monterey as the culprit. Looking online, I see that others are having similar issues with external media and Monterey. Apple, are you listening?