Airplay Display: How do I turn on airplay for macOS?

This option should only show if there is an Airplay display your mac could use.

Do you any available Airplay target, like an Apple TV in the same Wifi network?

Do you have any AppleTV or other Airplay device in your network? You only Airplay options when some target display is available.

macOS Catalina 10.15.7.

In system preference > displays > display

The dropdown menu for "Airplay Display" only has the off option when I click the dropdown. How do I get the on option?

Your mac does not become an Airplay target unless you add some third party software.

I have used AirServer for this purpose quite successfully.