The solution is stupid. If search is the problem, then break up search. Like literally fragment the company into a bunch of copies of itself so it is forced to compete against itself. And invalidate all patents the company has so none of the "children" own those either. Have some other safeguards so they don't just form back together in 10 years (or 50, or whatever, see the "Baby Bells" and such).
Competition is what causes good things in Capitalism. Don't just take away the way they're abusing something (Chrome), or give geographic monopolies (see Baby Bells above) but fragment the company itself, so you re-introduce real competition. Similar with Microsoft: breakup should have meant two (or more) companies distributing competing versions of Windows, not Windows vs Office vs whatever.
Honestly that could be an interesting pre-remedy: if you are subject to an antitrust verdict (not accusation, but conviction), all of your patents are invalidated, and all license agreements you are engaged in (i.e. patent owned by employee, but exclusively licensed to the company) are terminated. Make them afraid of losing their IP profile forever.
Anyways, that's a bunch of things thrown at the wall. I doubt they'll do any. But breaking off monopolistic pieces from the whole isn't the solution. Getting former parts of the company to compete in the same spaces is the problem.