Connecting new iMac with new MacBook Air

The 24" M3 iMac doesn't support being a monitor for any other device. Apple dropped Target Display Mode when the first Retina iMac came out in Late 2014. None of the iMacs that have nice Retina screens support it.

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You could set up the 24" M3 iMac as an AirPlay Receiver for AirPlay to Mac, then select it as an AirPlay display for the 15" MacBook Air. I believe that both Macs would support that.

I would not buy a 24' M3 iMac just to use it as an AirPlay Receiver. That way lies major disappointment. AirPlay is not as good as a hardware monitor connection. I don't think it will let you use that M3 iMac's 4.5K resolution, and there may be other video quality issues (artifacts, lags).

I mention it because if you had both Macs, for other reasons, it wouldn't cost you anything to play with the feature.

System requirements for Continuity features on Apple devices - Apple Support

Set up your Mac to be an AirPlay Receiver - Apple Support

If the applications that you are working with are present on both Macs, it might be easiest to keep the computers separate – and work on the project on both of them. There would be the problem of synchronizing updates, but there are ways to address that, like

• Storing working files for the project on iCloud Drive
• Storing working files for the project on a USB flash drive, which you move back and forth as needed
• Storing the original copies of photos in iCloud Photos

USB flash drives are easily lost, and do not have a reputation as the most reliable form of long-term storage, but if you backed up a "working" USB flash drive to one of the Macs and its backups on a regular basis, you could make things work.

Neither Mac can act as a monitor.

Both Macs are new enough to be AirPlay Receivers for AirPlay to Mac. So you could use the 15" MacBook Air as an AirPlay display for the 24" M3 iMac - with provision that the video quality might not be as good as if you were using a real hardware monitor.

There is also a way to create multiple desktops on a Mac – though you only get to see one desktop at a time.

Work in multiple spaces on Mac - Apple Support