When I started photography, this one took me ages to figure out, because people tend to explain it with a lot of math, or in a way that makes sense once you already grasp the principle but not before.

How does crop factor affect perspective?

It doesn't.

Not at all, in the slightest.
The only way you change perspective is to move the camera.
Changing the body or the lens has no effect at all on perspective.
What it affects is only how much of the overall image you can see through the viewfinder.

He was such a hit last time he appeared, I'm bringing him back for an encore.
The toy bear... & the bookshelf

I cheated making these so they don't actually overlay perfectly; I used a zoom lens, matched by eye in the viewfinder & later cropped to fit as best as possible - call it artistic license just to quickly demonstrate a point ;)
Click any image for larger version.

Here's our hero on a crop frame camera with an 85mm lens

Without changing the camera position at all, swap out the camera but not the lens.
85mm on full frame

OK, it looks completely different - but this is not a change of perspective, you can simply see more because the sensor is bigger.

Prove it by overlaying one image on the other...

Again without moving the camera, swap to a 120mm [approx] on the FF camera. You will see an identical image to our first shot - except for difference in depth of field, which will be slightly shallower. The framing & perspective will be identical.

Overlay darkened to show inset 120mm image on top of our 85mm image from above - it's hard to tell, but this is not a perfect overlay from the previous image, probably due to the very approximate nature of my method as well as the DOF change.

Then, to complete the experiment, swap back to the 85mm lens on the FF.
Now we can move the camera until we re-frame the bear as he was in the 'hero' shot from the beginning.

Now we've changed perspective, by moving the camera.
Even though we re-framed to match the bear in our original shot - the bear will almost perfectly overlay the first shot, except for the perspective change - the background is now totally different.