Why is it dominant? Is Google is preventing competition from entering the market or is it because Google offers the superior product? Good luck with that in court.
Of course it may not be prudent to go after a company that isn't doing any malicious against its competitors.
What would the punishment even be? Forcing adoption of other platforms to artificially inflate usage rates? Breaking Google Search into two competing Google Mini-Search products that aren't expected to cooperate and push search #3 and onward out of the market?
It’s probably about Google stifling competitors on their own search results page.
Yelp has complained forever that Google ranks their own reviews above Yelp.
Things like that.