Whenever I try to import a texture, the colors all become distorted and blurred (it's pretty much crucial this doesn't happen because I'm trying for a pixel art aesthetic). I have the texture filter set to nearest both in the Sprite3D settings and as the default in project settings. This fixed the edge of the pixels being blurred, but I can't find a way anywhere to fix the color distortion. I am using Godot 4.0.1.
As an example, this is a sprite that I tried to import into the engine (I checked the file and it's not messed up in any way):

And this is how it comes out in Godot:

Thanks in advance for any help!

Maybe try turning off mip-maps, that might help. Also make sure your image is a power of 2 (32x32, 64x64, 128x128, etc.), as that might also help a tiny bit. I'm not sure if either will make a big difference, but it's what I'd try first.

Try setting texture compression mode in import options to Lossless.

Am I seeing you using it in a 3D environment?
Perhaps it is lighting issue and playing with it can help?
If you are using it in 2D there shouldn't be any issue.