Don't upgrade to Monterey to attempt to fix your issue. You will just be making the troubleshooting process that much more difficult since you will be introducing a completely new OS which may or may not be compatible with your third party apps and external devices. You should resolve the issue with Big Sur first. If you want to reinstall the OS, then reinstall Big Sur over top of itself so it does not introduce complicated unknowns into the equation. A reinstall of Big Sur over top of itself is much safer and if that does not fix the issue, then upgrading to Monterey is even less likely to help and may even introduce new problems. Some users are still reporting compatibility issues with some USB3 drives even after the 12.1 update.
What file system is on the USB stick?
What brand are the USB sticks? Are they all the same brand? If so, then they may all have a similar issue. Like I said before the quality of USB sticks is extremely poor plus Macs can be a bit particular about the drives they use. At work we had a USB stick that would work on one Mac, but not on another Mac. In fact, we had trouble erasing the USB stick on the other Mac which did not create the file system. In the end I figured out the USB stick did have some odd issue as it also had issues with booting some regular PCs. Using that USB stick on one Mac did not reveal any issue with it.
Have you tried using a different USB port?
Are you connecting the USB stick directly to the iMac or to a Keyboard or to a USB hub? Make sure to connect the USB stick directly to the iMac.
Also try erasing the USB stick using Disk Utility. Select the whole physical USB stick to erase instead of just the volume so that a new partition table is created as well. Within Disk Utility you may need to click "View" and select "Show All Devices" so that the physical USB stick appears on the left pane of Disk Utility. The physical drive will usually have the make & model of the drive listed which is the part you want to select (such as SanDisk Cruzer). Erase the whole physical drive as GUID partition and MacOS Extended (Journaled) if the drive will only be used with a Mac, otherwise erase the whole physical drive as GUID partition and exFAT if the drive will be shared with Windows.
Try disconnecting all external devices in case one of them is interfering.
It is also possible you have some third party software installed that is interfering with the normal operation of macOS. Typical causes of problems are usually due to anti-virus apps, cleaning apps, and third party security software. None of these types of apps are needed on a Mac and usually cause more problems than they solve plus they impact system performance. Try booting into Safe Mode to see if you can transfer the file. If Safe Mode works, then some third party app is most likely causing the problem (or perhaps an external device).
I highly recommend you have a good backup before proceeding any further.
You should always have frequent and regular backups of your computer and all external media which contains important & unique data.
