Extend Display between iMac and MacBook Air

I have an iMac (M1, 2021) and a MacBook Air (Retina Display 2018). I would like to extend my desktop across the multiple displays and use either screen like a monitor. When I connect them with a USB-C cord, a notification pops up on my Mac that says "Cannot Use Thunderbolt Accessory. Connect accessory to a Thunderbolt port on this Mac." I've done that but nothing seems to be working. I have also tried using a Thunderbolt 3 cord with no luck. Is there any way I can connect the two displays and use either computer screen like a monitor? Online says that it may not be possible since my iMac is a newer model. Are there any other options to make this possible, or any alternatives to achieve similar results that aren't buying a separate display ?