Using iMac 27-inch late 2015 as a second monitor with my MacBook Air M1 2020

Your question comes up often and the answer does not vary. iMacs are computers, they are NOT external display for other devices. What works in Target Display Mode is VERY limited and both of your devices are too new to work in Target Display Mode. Please carefully read Target Display Mode and you will see.

Also note that a 2015 iMac is very obsolete, will not run current versions of Mac OS and is also considered vintage meaning parts are largely unavailable for it. If it work, keep it as a toy, however if the computer was not setup per What to do before you sell, give away, or trade in your Mac then return it as it will always be tied to the original owner and will be a source of frustration.

Target Display Mode went away when the first 27” 5K Retina iMac came out in Late 2014 - and never came back. Your Late 2015 iMac does.not have it and cannot act as a hardware monitor for another computer.

That iMac is too old to support being an AirPlay Receiver for AirPlay to

Mac (a lower-quality connection method).

There is a third-party workaround called Luna Display, by Astropad, that might let you use that iMac as a.second display, it may cone with significant compromises, and even Astropaf does not recommend it for high motion applications such as gaming and video editing.

Repurpose, sell, recycle the 2015 iMac and get an aftermarket external display to use with the MacBook Air.

Use an external display with your MacBook Air - Apple Support