It sure sounds like racism and poorphobia to me. HR trying to make sure her surroundings don’t look like what a “typical poor person” would have (clutter, children, signs of disability, “drugs”, etc.) It’s not super common, but it’s common enough that I hear about it every so often.

I can’t offer any kind of legal advice, but it sounds like this job will be potentially problematic and HR will definitely be one to watch out for.

ETA: There’s a lot of paranoia in the US right now about “laptop farms”. Remote jobs are paranoid about people getting remote work to send money back to North Korea. It’s completely ridiculous, and it’s causing issues for a lot of people, mostly marginalized people. I think it’s useful context to know why this kind of thing is happening more lately.