I had a slightly different USB storage device not mounting, or appeared to not mount. As a creature of habit I would always to the Finder>Locations to copy photos from my Flir C3 camera. That was the easiest location. After the Big Sur update it stopped being listed. For a few weeks I resorted to using my 2012 MacBook Pro that does not support Big Sur to transfer and sneakerNet the images to my iMac.
Then I happened to notice the device was in fact being displayed on my desktop. I just had not noticed (clutter and all) It worked fine but still not listed in the under "Locations" in Finder my goto.
It always displayed as "Untitled." On a whim today, I renamed it from Untitled to FlirC3, ejected it and reattached it. Low and behold FlirC3 is now listed in Locations. There must have been a change, likely security related that does not allow "Untitled" devises to be listed in Locations