Cannot share screens between an iMac 21,5" and an iMac 27"

Malcolm, you are correct if you are trying to use Target display mode. DuetDisplay and LunaDisplay allow you to extend/mirror your screen on another Mac. I'm doing this with DuetDisplay on a 2012 27" iMac and a 2020 27" iMac. I would prefer to be able to use target display mode.

Paul

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

"You can connect any of these older iMac models to another Mac from 2019 or earlier for use as an external display."

Does screen sharing work between other macs? Have you gone through these steps yet?

https://support.apple.com/guide/mac-help/share-the-screen-of-another-mac-mh14066/mac