I have Parallels 19.3 on my 27-in iMac in another room and on the same network segment as my M2 Mac mini Pro. On the iMac, I have just screen sharing configured, and on my M2 Mac mini, I copied the Screen Sharing.app onto my Dock. In the Finder, press shift+cmd+G (Go to Folder), copy and paste the following path, and press return. That will open a new Finder Window on that location.
/System/Library/CoreServices/Applications
That is where the Screen Sharing.app is located.
With your iMac powered on, you click that Screen Sharing.app in the Air's Dock and it will launch a panel where you enter the hostname.local (use your iMac hostname) and connect. You will be making a VNC (virtual network computing) connect between your two Macs, and depending on the speed of the Wi-Fi (or Ethernet is better) connection, you interaction with the iMac may be fine or slow.
The following is Windows 11 Pro running in Parallel's Desktop on macOS Monterey from my iMac displayed on the 32-in LG 4K display of my M2 Mac mini over Wi-Fi 6. You would shut Windows down normally and return to Parallels panel. Quit Parallels, and when you shutdown the iMac through its screen sharing interface, you will see a spinning globe on its Desktop. You then visit the Air's Screen Sharing app's Connection menu, select Close, and then quit the Screen Sharing app. The iMac will be powered off.
