The issue of you already buying something is interesting to me. It’s so obvious that they’d fix it if it cause revenue loss. My guess is that conversion for any ad is so low that you’re indeed more likely to buy a lot of products twice rather than buying something totally different.
No, it's really difficult for 'them' to find out whether you actually purchased something. All the tracking stuff is on social media and the product browsing pages. But not on checkout. Shopping sites can't allow all that stuff there because of security and privacy issues. So big tech doesn't even know whether you bought something. They only know what you have seen. That's why they keep showing it.