I wouldn't worry about automated ATS. Their use is way overstated on LinkedIn, by "resume experts," etc.

I'm talking about whether a human can read the document comfortably.

Do you have any tips, code, or even just a list of the common ATS systems? I need to do this with my latex cv but I'm not even sure where to start.

I don’t know of the example systems but I’ve applied to a handful of companies recently, all running the same-ish workday resume ingestion. You can actually tell which are running a more recent version because the parsing is more accurate.

There is also a common no-account single page application software, I checked at a company I’d applied to and it was called Lever(?)

Normally, I thought for ATS parsing if you upload in an application and a few of the prior experience text boxes are accurate, then you’re good. I’ve always had to fix my experiences though, even with using a word doc.

I think this open-source parser details a typical ATS algorithm: https://www.open-resume.com/resume-parser