The printer can be connected via Wi-Fi or Ethernet (to the Wi-Fi router).
The Mac mini can use Wi-Fi or Ethernet to the router.
The printer and the computer must be connected to the same network (Wi-Fi router).
If there is a problem with AirPrint discovery for one or more devices, and if all settings are correct, you may want to try the following full procedure (in the exact order):
Power off the Wi-Fi router, the printer, the Mac mini, and all other devices/computers. Wait two to three minutes. Power on the router. Wait two to three minutes. Power on the printer. Wait a minute or two. Power on the Mac mini. Finally, power on all other devices/computers.
Add a printer on Mac – Apple Support (UK)
Reset the Mac printing system to solve a problem – Apple Support (UK)