How to use an iMac as a second display?

I'm trying to use my older iMac 2012 (running Catalina) with a thunderbolt connection as a second display for my 2020 iMac running BigSur. I've connected the two and the F2 does not work. (I've tried all the F2 simple fixes, different keyboards etc). The older Mac will be recognized by my MacBook Air (2018) and work as a monitor (So I know my USB-C to thunderbolt adapters, all $100 worth, are good) but my new iMac running BigSur will not detect it. Has my old Mac become useless and obsolete now?

Thanks,

RB