iMac as display for new M4 Mac mini.

The iMac cannot be used as a monitor for any of the newest Macs and Target Display mode is no longer a feature of macOS, having been deprecated years ago.

Please see: Use your iMac as a display with target display mode - Apple Support

Per the link above:

• Your target iMac (monitor) must be using macOS High Sierra 10.13.6 or earlier. 

• In all cases the source Mac that you're connecting FROM must have been introduced in 2019 or earlier and have macOS 10.15 Catalina or earlier installed.

You might consider a third-party solution - Luna Display or Duet Display - though the performance of those options is limited and really not suitable for motion images. Regardless, you still will need a proper monitor to set up either of those options.

Do yourself a favor, avoid the headache and just budget an extra $100 for a monitor. Yes, they are that inexpensive.

No it cannot. If you want or need a 2nd display for the new M4 based MM you need to buy one. Please remember iMacs are computers, they are NOT external displays for other devices!!!