They are primarily an information marketplace, and offer people free services so that they'll participate in that market.
Their secondary interest is in things like Adsense and in products like Doubleclick, which are where you worry about tracking and them building a behavioral persona of what you do across the entire internet.
However, Google doesn't need to even see this persona themselves - they just want to get the best ads in front of you to make marketing departments happy. Ideas like "privacy sandbox" are partially driven by this desire - give Google the value of gathering and correlating existing data and more, without the brand impact or risks of holding that data themselves.
The thing they give up is the ability to do cluster analysis across people/demographics to understand where and why an ad is performing. Targeting of advertisements remains a manual process and not a machine learning driven one.
It's obvious, but I want to make clear, that this doesn't make Google less scary or more trustworty. Avoiding Google is still advised imo.
edit: replace "private" with "to themselves"