Using MacBook Air as a second monitor for iMac (Retina 4K, 21.5-inch, 2019)

MacBooks of any flavor have never been able to function an external monitor. Only a small sub-set of iMacs between Late 2009 and Mid 2014 could be used via Target Displays Mode.

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

There may be network screen sharing options available to you but those often have either resolution, lag issues, or both.

Share the screen of another Mac - Apple Support

I haven't tried it, but Turn any Mac or iPad into a second display...

https://lunadisplay.com/

Review by NAK005, you may not be happy with it…

https://discussions.apple.com/thread/251259038?answerId=252422503022#252422503022

No. Only 2009-2010 27” and 2011-mid 2014 iMac’s supported Target Display Mode.