You should not have to do anything with USB drivers inside the Synology DSM operating system since it will only “pass-through” to the VM, but you do need to get Synology Virtual Machine Manager to see the USB device so can mount to the virtual machine, however, you not seeing it there under the virtual machine in Synology VMM to mount it is probably more likely a problem with the USB dongle itself of the USB extension cable that you are using for it.
The enclosure/chassis/casing design of some computers (and NAS:es) makes it so that the USB plug on some USB dongle are slightly too short so could be that you can not physically plug the dongle all the way into the USB port in order for it to get proper contact, (as the chassis is basically in the way).
Some enclosures/chassis/casings are very thick so some USB adapters can not make physical contact and others have the board for the USB port to far inside the enclosure which makes it hard to adapters with short USB plugs without using a USB extension cable that has a little extra long USB plug to get plugged in further. For example, if you search then you find that many USB adapters have this issue with the Home Assistant Blue enclosure/chassi/casing and the solution there has been to use a USB extension cable with “longer” plug.
That is, the USB adapter plug is a little too short which makes it harder and sometimes impossible to plug it into some USB ports if the computer enclosure/chassis/casing is too thick around the USB-port as that will physically prevent the USB dongle from actually making a proper connection inside the USB port even if it looks like it is plugged in all the way that is possible.
If that is the issue to work around it you can use a different USB extension cable that has a longer USB plug than what the dongle has on its own, or better yet, connect it via a powered USB 2.0 hub (with a USB cable that has as a longer USB plug) as you should really be doing that anyway if your Synology only has USB 3.0 ports (as connecting to a USB 3.0 port without going through USB 2.0 hub can cause serious interference to Zigbee and Thread as well as Bluetooth radios, while connecting via a USB 2.0 hub will practically convert one USB 3.0 port into many USB 2.0 ports which do not have the same issue with interference).
Regardless, read and follow → Guide for Zigbee interference avoidance and network range/coverage optimization