Is it possible to use a Mac Mini with the display of an iMac?

Only if both the Mac mini and the iMac meet the old Target Display Mode requirements.

carefully read > Use your iMac as a display with target display mode - Apple Support

For example: the new M1 Mac mini does not meet the Target Display Mode requirements and so you will need to use an aftermarket display with it.

see > Connect a display to Mac mini - Apple Support