Why is my pattern/texture on my UV crooked? As far as I can tell, my actual geometry isn't crooked

I don’t see any problem…

The right image on the top, the pixels are crooked instead of straight across.

You need to add more geometry. Preferably by making it composed of quads and triangles.
Ngons and UVs don’t play nice.

Yeah, just use the knife tool in edit mode to join those corner verts, and make everything quads. Ngons are never a great idea.

I’ve never had a problem with properly-mapped ngons, although I’m still new to Blender.

Make sure you don’t have duplicate verts somewhere skewing the image. You should have 8 edges and 8 verts when you select all. (I managed to do exactly this just trying to demonstrate my point, and had 12/12 when I initially wrote this.)

Here, it looks like everything is fine, but I have several extra verts in there, with one in particular skewing the edge.

I can’t seem to replicate your exact image, but I suspect it’s some kind of duplicated geometry.

You can see statistics in 2.9 by clicking the Viewport Overlays icon, and ticking Statistics.