Using 2015 iMac as a display monitor for new MacBook air

Not Natively, no.

You can use something like Luna Display, but there will be some lag. It should work for more static things like office work, web browsing and email and should be fine. https://astropad.com/product/lunadisplay/

As to why not? We cannot say. Speculating on Apple's decisions is not allowed here. There's no reason to believe its not a technical limitation however.

The reason: both devices are far too new for the now-deprecated Target Display Mode (TDM).

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

It's dead tech.

For the US$80 cost of Luna Display you can find often find a decent eternal monitor on sale that has numersous advantages over using the iMac as second monitor, including no lag.

Apple dropped Target Display Mode from new Macs in Late 2014 – when the first 27" Retina 5K iMac came out. After that, no Macs had it (even the 21.5" ones).

Not possible, unfortunately. Apple has discontinued the feature because the iMac is a computer, not display. Buy a dedicated monitor instead.