I assume GP means to split Search but keep search ads, called "AdWords", together with it. The third-party advertisement part of Google was/is called AdSense. The two were always run separately AFAIK.

By running ads. Probably Google Ads. What it's already doing.

I thought that the ads on search were a nice to have, but that the real value of search was the profile it allows google to build about a person, which is then used by all ad systems used by google.

Split that off, and search is all of a sudden producing a whole let less value, since the profiling value cannot be meaningfully extracted by other companies.