Connect iMac late 2012 as a second monitor for Macbook Air M2

Not as a Target Display Mode display. The 2012 iMac supports Target Display Mode, but current restrictions on Target Display Mode make it useless.

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

1. The Late 2012 iMac has to be running High Sierra or earlier. You're running Catalina.
2. The other machine has to be a Mac introduced in 2019 or earlier, running Catalina or earlier. The M2 MacBook Air came out in 2023 and can't run any version of the OS that old.

AirServer may suit your purpose. It allows older Macs to act as an AirPlay Receiver. There's a free trial.

https://www.airserver.com/Mac