The project page says the recommended size for a cover image is 630x500 - but I don't see cover images displayed anywhere near that size anywhere on the site.

Where does that recommendation come from?

What sizes should I be targeting?

What scaling algorithm does itch use?

This is of some concern for someone who wants detailed pixel art in their cover image - I want to be able to tell someone I'm contracting to draw one how to make sure it looks good at the sizes it ends up getting displayed at.

I suspect the double size is displayed to people with 4K monitors.

If you're using pixel art for your cover then you should probably be using 2x, 3x, or 4x pixel size in the image depending on the art. The scaling algorithm should have limited effect on the pixels at larger ratios. We do use a filtering algorithm on server side resize, and also your browser will resize images. Only the aspect ratio is provided, but you should have a suitable size to prevent upscaling.