The Luna Display acts as a normal display connected to the GPU.
You can only connect one normal display to a M1 Mac's Thunderbolt ports. You can connect another display to the HDMI port of the M1 Mac mini.
What is your external display?
If you don't have the HDMI version of the Luna Display (it's not available yet and it will only be available for Windows?) and you don't have a HDMI port on your display, you can try converting HDMI to USB-C using the Club 3D CAC-1332. There's also a version of the adapter from SIIG and probably others. I don't know how well it works on M1 Macs (especially since Apple removed EDID overrides on M1 Macs).
Once you've connected two displays (one to HDMI and the other to USB-C) then the only way to add additional displays is to use a DisplayLink adapter. Display's connected to DisplayLink are not connected to the GPU so they do not perform as well (DisplayLink compresses video over USB).