The remedy document does not ask this.
What you cite after "> As detailed in..." does not ban any and all payments from a search engine (or only from Google) to a browser. The remedy doc is based on the antitrust case's finding that Google violated U.S. Law by abusing its monopoly through "tying", and in particular by forcing partners to lock out competitors through exclusive (default search only) deals.
This does not mean Google cannot pay for search traffic, and indeed Google has a relatively open, albeit lower-monetizing, system called Adsense for Search, which allows a toolbar to monetize -- but not a browser via queries entered into its address bar (aka Omnibus). Bing does many API deals, or did (it hiked prices last year). Brave has an API business (not yet an ads feed, just search).