Using iMac as a second screen for MacBook Air

Sorry, no, an iMac has no external input ports to use as a display. In the past there was a feature called Target Display Mode that allowed this but that feature was removed long ago.

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

Your 2017 iMac does not support Target Display Mode. You should consider purchasing a dedicated display for use with a MacBook Air 2025.

No. The Target Display option is not supported on either of those Macs sorry.

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

Nope. The mirroring option requires a 2018 or later iMac.

Sorry.

click here ➜ Stream video and audio with AirPlay to a Mac - Apple Support

There is a workaround product called Luna Display that might let you reuse that 27" iMac as a second display. But even the Astropad site acknowledges that it has limitations and is not recommended for high motion content such as video editing or gaming. Another issue is that you would need to make two connections to the MacBook Air and the MacBook Air only has two multi-purpose USB-C ports.

The main reason this is attractive at all is that – even now that there are several 27" 5K displays on the market, they are still relatively few and expensive. Probably at least $800 – $1200 USD for a third-party one, and $1599+ USD for the 27" Apple Studio Display. On the other hand, you can get decent 27" 4K displays with IPS panels and near-100% coverage of sRGB for as little as $300 – $400 USD. That might be the way to go if you are on a budget.