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

No, you cannot.

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

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/