Most of the "3D" we see is made up by our brains. For evidence of this, look at a photograph, and look at how far away things are.

Having eyes spaced apart does help us to tell the distance to things that are close to us, but that is only useful for a short distance. Our brains also track the parallax and occlusion of numerous objects, which helps over longer distances, but works just fine with 1 eye.

I think there are two ways eyes could work in higher spacial dimensions, you could either have an n dimensional eye, which percieves an n-1 dimensional image, and then an understanding of "distance" is used to fill in the remaining information, or (which may just be my own 3D-ness showing) you could have several 3D eyes in different directions, each percieving different 2D images, with enough overlap to fully see the n-dimensional space. That would take n-1 eyes to properly see.

You can see depth with a single eye, you just need to move your eye

Two eyes in animals are used either to get extra view angle (in a cow, for instance) or to give instant depth information (in a human or tiger for example) or for both (in dragonflies)

I always knew that spiders were from the ninth dimension.

You can get depth information from parallax, which can come from either capturing multiple moments or using multiple viewpoints. IDK if I would call this seeing in 3D, as you can still only see 2d surfaces, just with an additional data point of depth (Think of it like an array of data, with one eye, you get res^2 * (r+g+b) data points, with two, you get res^2 * (r+g+b+r+g+b+d) instead of actual 3D which would be res^3 * (r+g+b)). Having 3 eyes just means you can estimate depth more accurately. Of course, in real animals with many eyes the eyes serve different purposes, such as having a different fov, resolution, color perception, etc.