The dongle is definitely not using Bluetooth. Wireless peripherals with USB dongles generally have their own custom radio protocol, for better or worse.
Before later revisions of Bluetooth with ultra-low-power modes, a mouse using Bluetooth was considerably more power-hungry than dedicated radio interfaces -- short battery life.
It needed to charge multiple times per week in a cradle and always indicated the battery life when it was moved around.
It would die in the middle of playing DotA, so I had two and would pause the game with the admin commands on my host bot for just long enough to pull the waiting one out of the dock and press the pairing buttons. Fun times lol.
A physical OEM USB dongle on PC side, whether Bluetooth or not, and an On/Off switch on the peripheral side would have certainly prevented the issue in discussion.