Most of them use Bing's indexes on the backend and some competition does not mean that Google doesn't have monopoly power over the market. Firefox exists but Chrome still has a much larger share of the market.

Just because something has monopoly because of being better shouldn't result in antitrust. Even in the browser case, Google is very active in standardisation, and also pays Firefox. Though I think we should definitely ban things like Google search engine advertising Google Chrome for free.