Straight forward with no depth perception.

Ah. But your character sometimes moves his eyes.

As a disc flattened from overhead. You would see straight up in the air
but not from side to side.

Thinking about it working like a camera, with distance between the back of the eye and the pupil creating a certain field-of-view, then if it's flattened, it might be more of a fish-eye-lens effect, where your vision is much wider since the focal distance is much smaller.

Yeah. thats an interesting thought. And maybe the sight might bend when they bend their head