Well you're never going to believe this, but I found the culprit: Western Digital's "WD Security" package and its "WD Drive Manager" service.
The big clue was that the problem went away entirely in Safe Mode; it just took me a little digging to figure out how to get this system into safe mode, because the usual method of shift-clicking the power menu in Windows 11 didn't work for me (my system drive is a RAID 1 array, and the Windows Recovery Environment/WindowsRE couldn't see or boot the system partition, but changing the boot method to Safe Mode in msconfig did work; also boo to Microsoft for dropping the F8 capability).
I started by noting which devices did not get drivers loaded in Safe Mode in the Device manager, then disabling them one by one after a normal boot, but this did not change the behavior. Then I tried the most obvious culprits: my anti-virus software (ESET) and the protection services in my backup software (Acronis). No luck here either. Lastly, I started going through non-Microsoft services from services.msc which were running as Local System, stopping them one by one as I repeated the test. After I stopped "WD Drive Manager" the problem went away immediately and completely.
I don't know what WD Drive Manager is doing, but I'm guessing it must be listening for / filtering all USB events all the time, and when it gets too busy with a large amount of data being sent to/from an external drive, it starts dropping events for other devices. It's pretty horrendous behavior, and this service is now stopped and disabled on my system until I need to unlock my old backup drive again.