Earlier quoted context omitted.
That's just how context works. If you visit another site then there would be different categories involved and has nothing to do with the user. There's also no personal identity, it's just a cookie if available, used mostly to frequency cap.
Can't adtech companies associate that cookie with the category and build a profile over multiple pages? Then they can correlate the data and identifiers Google provides to any that they collect on their own (e.g. their own pixels served in the ads that actually get shown). If they connect their own pixel identifiers to data that they buy, then they are building up a decent profile.
Cookies are also not an identity and refreshed very often. Their main use is to cap ad frequency and track conversions over the short-term (hours to days).
Google and Facebook do not provide any personal identifiers. That would be a massive breach of their core 1st party dataset. What little data they did provide is now gone with GDPR.