While Projector is a compatible app that is available in the visionOS App Store, there are some practical limitations when running Projector on the Apple Vision Pro.
First of all, the Vision Pro does not (as far as I can tell) have the ability for a running app to "connect to an external screen". That is the technique that Projector uses to display the slides to a connected AirPlay or HDMI device on the iOS and iPadOS platforms.
Because of this current limitation in visionOS, the most likely use of Projector on the Vision Pro is to be the Sessions controlling device. You can start a Session on Projector and then connect to that session with other devices running Projector. The Vision Pro instance of Projector can then be used to control the slide behavior on the other devices.
As Apple continues to implement new visionOS features, Projector will take advantage of them, when available, with subsequent Projector releases.