Raycaste vs trigger Colliders & Rigidbody performance

The ultimate performance is to do no calculations at all. For such simple case, as a spinning wheel you can know your sector using local rotation angle.

int Sector = MathF.FloorToInt(rotation.x / NumberOfSectors)

As for the general quastions linecasting, raycasting and especially spherecasting generally performe significantly worse than OnTriggerEnter/OnTriggerStay, because Contact detection uses nice algorithms, that discard noncolliding bodies early, and don't even start unnecessary calculations.

With linecasts inside your update you evaluate the situation every frame, against all the objects you have.

None of this is written in stone actually. For example, If you manage masks good enough, so you check only against few items, and have thousands of triggers on the scene, you can have linecasts work faster than OnEnter/OnExit. Always check, what's profiler saying.