Can the iMac (21.5-inch, Late 2013) be used as display with M4 Mac Mini?

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Yes, a late 2013 21.5-inch iMac can be used as a display for an M4 Mac Mini if you use Target Display Mode and the correct cables. However, the iMac must be running macOS High Sierra or earlier, and the Mac Mini must be running macOS Catalina or earlier. 

How to use Target Display Mode

1. Connect the iMac and Mac Mini with a Thunderbolt or Thunderbolt 2 cable. 
2. Make sure the iMac is running macOS High Sierra or earlier. 
3. Make sure the Mac Mini is running macOS Catalina or earlier. 
4. On the iMac, select Apple menu > System Preferences > Keyboard. 
5. Ensure that Use F1, F2, etc. keys as standard function keys is not selected. 
6. On the iMac, press Command-F2. 

If Target Display Mode doesn't work, you can try these steps: 

• Log out of the iMac and then press Command-F2 again.
• Use the keyboard that came with the iMac.
• Boot the iMac into safe mode.