I got my new Mac mini today and this was the first test I did to see if I have this issue:
1) connect a USB 3.0 HDD directly to the mini
2) configure it as a Time Machine backup drive
3) start the backup process
Sure enough, as soon as the system started accessing the HDD, my wireless trackball went bonkers AND, even more frustratingly, my Bluetooth keyboard (Filco Minila Air) which I have been using with all my computers since 2014 without any issues whatsoever, started skipping keypresses.
I know I could possibly solve the problem by buying an external dongle, but honestly, at this price (I paid 1800 euro for my Mac mini) it should be damn perfect.
Seriously, what's wrong with Apple? Wi-fi inside my 2016 MacBook Pro turns into a potato when I connect it to my USB-C docking station (connection speed drops from 867 Mbps to less than 100 Mbps), and this Mac mini seems to have a crappy Bluetooth module. No bueno.