From what I understand, OpenXR is a common interface that needs to be implemented by the headset manufacturer. If Apple doesn't do this, OpenXR apps won't work.

Before OpenXR every headset had its own interface. Valve and descendants have SteamVR, Oculus has its own runtime, Microsoft and descendants have Windows Mixed Reality.

Games/Apps targeting these platforms used to have to implement each one of these interfaces separately if they wanted to support that family of headsets. OpenXR shifts the responsibility onto the headset manufacturer, from my limited understanding.

This is the correct answer, despite being downvoted.

What’s technically preventing OpenXR apps from working? Vision Pro doesn’t implement OpenXR.

In principle it might be possible to build an OpenXR compatibility layer on top of Apples APIs, similar to how MoltenVK implements Vulkan on top of Metal, but impedence mismatch between the APIs means that may never be completely seamless.