Steve
Is the keyboard the Older version with removable batteries or the Newer without removable batteries? As a temporary workaround and to get access to Utilities on the Mac mini - use a wired keyboard.
Now, if the keyboard is Older and has been used previously with another device - it needs to be Unpaired from the previous device. With the usb keyboard attached and the now Unpaired Keyboard available turn it Off. Pause maybe 10 seconds and turn it On again and see of the new Mac mini can see it and pair it.
If the keyboard is the Newer without removable batteries and again using the USB Keyboard - use the Lightning to USB cable that came with the New Keyboard - connect to keyboard and then to Mac mini - it should comment the Pairing process