How can I copy data from broken iMac
I am trying to help out a friend with their Intel iMac running Monterey. It currently won't boot and hangs part way - tried Disk First Aid but looks like I need to copy data and reformat. They have no back-up (yes, I told them they needed it) so hoped I could use Target Disk with Thunderbolt cable to connect another Mac. The latest OS I have on a Macbook Air is Mojave but when I try this it says the iMac disk is incompatible. I cannot install Monterey on an external HD on the iMac - it says disk needs formatting in AFPS and the HD won't do this in Disk Utility. All I need is to be able to copy the data from the iMac and I can reformat the drive and hopefully fix it, but it seems the changes to disk formatting is making this tricky.
The Mac running Mojave isn't mine, so not keen to update this unless necessary. Any suggestions gratefully received. Thanks.