What can I do with a 27", Late 2013 iMac??

JPEGjunkie wrote:

How were you able to use your 2013 iMac as a display for your m2 machine? Did you have to do anything special for it to show up with screen sharing? Currently trying to get my 2013 iMac to work as a display for my m1 MacBook and not finding anything helpful

The person to whom you are replying said that 'When I need to access the iMac, I power it on and connect to it via Screen Sharing from my M2 Mac mini Pro running macOS Sonoma 14.4.1."

I believe that that feature would have allowed him to view the iMac's screen in a window on the M2 Pro Mac mini's screen – so he could operate the iMac using the keyboard, mouse, and screen belonging to the M2 Pro Mac mini.

It would not have made the 2013 iMac a second display for the M2 Pro Mac mini. You might be thinking of Target Display Mode. The 2013 iMacs support Target Display Mode using Thunderbolt input – but Apple put restrictions on "the other Mac." It must be a Mac released in 2019 or earlier, running Catalina or earlier. That means that your M1 MacBook is too new to use your 2013 iMac as a Target Display.

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

Your 2013 iMac is also too old to serve as an AirPlay Receiver for AirPlay to Mac. AirPlay is not as good as a Target Display Mode connection or a connection to a real hardware monitor. Still, because AirPlay from Macs was around long before AirPlay to Macs, there is a possibility that you could set up your M1 MacBook as an AirPlay receiver and use it as an extra screen for the 2013 iMac. (I know, not the direction you were hoping for.)

System requirements for Continuity features on Apple devices - Apple Support

Set up your Mac to be an AirPlay Receiver - Apple Support

There are third-party workaround products (Luna Display, Duet Display) that might let you use your 2013 iMac as a second display for your M1 MacBook, but the connection won't be as good as with a real hardware monitor. There is little likelihood that it would be worth it to reuse a 21.5" 1920x1080 iMac screen, and even if that iMac was a 27" one with 2560x1440 resolution, the cost of real 27" 2560x1440 and 27" 3840x2160 monitors is low enough that getting a decent 27" standalone monitor would make you a lot happier.