Are you connecting the USB stick directly to the Mac?
Try booting into Safe Mode to see if you have the same problem just in case you have some third party software installed that is interfering with the normal operation of macOS.
What file system is on the USB stick?
Within Disk Utility you may need to click "View" and select "Show All Devices" in order to see the physical drive on the left pane of Disk Utility. If you don't see the physical drive on the left pane after doing this, then there must be some sort of compatibility issue. Disconnect all other unnecessary external devices in case one of them is causing a problem. macOS Monterey has had a lot of reported compatibility issues with each update patch so it would not surprise me. The quality of USB sticks is also very poor and I have seen compatibility issues and reliability issues even if the USB stick works with many other systems.