using 27" imac as monitor for M4 mac mini

That iMac doesn't support Target Display Mode. Target Display Mode went away when the first 27" 5K Retina iMac came out in Late 2014, and never returned.

Apple also added restrictions so that new Macs like your M4 Mac mini do not support using ANY iMac (even an old one that does support TDM) as a Target Display.

+1 nope simply will not work! You need to purchase an external display, don’t worry you can find them anywhere from <$100 to $1500 and everywhere in between. If you budget about $350 you can get a very nice 4k 27”-32” display.

No, it is unsupported. Purchase a real external display for the M4 Mac mini. I use a 32-in LG 4K UltraFine display with this Belkin HDMI 2.1 cable.

No, and Using an iMac as a monitor - Apple Community explains why.