M4 Mac-mini, Samsung M8 monitor; how do I access the camera on the Samsung display?

If you're unable to get the Samsung camera working with your Mini consider using your iPhone (if you have one) as the web cam for the Mini: Continuity Camera: Use iPhone as a webcam for Mac - Apple Support

Just some food for thought.

to use an external webcam be it in a monitor or just by USB cable you will need a driver for macOS

if Samsung only have a windows driver for their monitor cam then you will never be able to use it, and you no matter what will likely be required to connect the mac to the monitor by more than just a HDMI or display port cable

What type of cable are you currently using between the Mac mini and Samsung display…?