I have a ... "Terabyte 100031N Ultra Slim Wireless Mouse (Black)"
This mouse does not use Bluetooth at all. It is simply a "wireless" mouse that uses some sort of proprietary 2.4 Ghz signal to communicate with its USB dongle. That means you can not connect any Bluetooth device to the dongle for that mouse. It is unlikely that you can even use that dongle for another mouse of the exact same model!
Was wondering if the controller needs specific Bluetooth dongle?
The Xbox One controller supports either the proprietary USB adapter (for all wireless controllers), or some newer controller models support Bluetooh 4.0. Bluetooth is a wireless communication standard, so that means any Bluetooth 4.0 dongle will work for those controllers.
Only the Xbox One S controllers can connect to a Bluetooth dongle. Here is a guide to help you identify if you have the correct type of controller.