Monterey or Silicon Macs have trouble with select attached storage- especially attached HDD storage. I've had too many rounds with the almost opposite problem- "unexpected eject"ions- by HDDs attached to a new Studio Ultra that are absolutely stable on Intel Macs running macOS < BigSur and using the same cable. I'm far from the only one- there are MANY threads here and elsewhere about this with people trying everything. I've worked through everything a user can and concluded that there are bugs in either Monterey and/or with Silicon itself with select HDD enclosures/hardware. Some will work perfectly fine. Some won't. SSDs seem to generally work better than HDDs but even some of them have such issues too.
Basically U in USB doesn't appear to mean what it is supposed to mean with Silicon or Big Sur-Monterey. More like MSB for Maybe Serial Bus.
There does not seem to be any way to determine which enclosures work except try attaching things and see what happens... and what will
stay attached.
OP, my suggestion is to duplicate all 3 partitions to another disk, reformat that problematic drive and then, before you start copying anything back to it, see if it will mount pretty quickly as a blank. Based on existing Intel Macs, 10-20-30 minutes is ridiculous UNLESS there is something wrong with the HDD or enclosure. In testing to try to solve my issues, I dug out ancient tech and pretty much everything will mount in under 30-60 seconds... even stuff from the 2000s.
If you "clean" reformat and it mounts quickly as a blank, recreate your partitions and try again (while all 3 are still blank). If that mounts about as quickly, copy your files back to each section... maybe just one at a time and again, unmount-mount. If you get this far without issue, maybe you discover the files in one partition are somehow causing this? If so, dig into what is "different" about those files.
If a clean, blank HDD won't mount quickly, maybe try a
different enclosure if you have one. That will help you narrow in on enclosure vs. drive. For example, if you put it in another and it mounts much more quickly, the former enclosure appears to have problems. On the other hand, if you move the drive to another enclosure and it is the same slow mount, the HDD itself appears to be the issue.
One more test: if you have existing Intel Macs, test on those too. If it mounts much more quickly on Intel Macs, you are probably enjoying the Silicon and/or Big Sur-Monterey
MSB "fun." Welcome to the club! All hail the Apple!
You might have to do what I did and just start trying
various enclosures until you find one that works with seemingly finicky Silicon and/or Monterey. If you have to go here, I found
OWC MiniStack STX mounts quickly and stays connected. It can handle a 3.5", 2.5" and/or M.2 stick.