Can I use my late 2013 27" iMac as an external display with a new M1 iMac?

You're welcome.

AirPlay not yet.

However Apple have previewed AirPlay to Mac as a feature in the upcoming macOS Monterey, so keep an eye out for that.

https://www.apple.com/macos/monterey-preview/features/

No, you cannot.

The feature is not supported in the new M1 Macs. Nor is it supported in macOS Bug Sur.