I don't think there's a pre-built FPS VR template from Unity, but it is pretty simple for basic projects. Word of warning, though: VR locomotion is very different from FPS locomotion, and gets very complex pretty quickly.

Ah, that’s a shame. I naively thought the Unity FPS game would load onto Oculus Quest.

My real goal is to have students ship content of their own to the Quest, to dive a little deeper into programming and technology than they might do as mere consumers.

Currently you could sideload it or work with the Oculus submission process to release it on their store. This article seems to suggest they will release another, frictionless avenue to make VR experiences accessible on Quest.