a monopoly is not defined by the things you list. it is instead defined by the ability to exert disproportionate power on a market, enough to create favorable conditions for itself (i.e., it's anti-free market).
it's usually characterized by a large, but not necessarily majority, market share in a given industry or segment (monopolies can have as little as 30% market share), and pricing power, both of which google has in search.
But this is true of all websites. Are you suggesting that AdWords (not AdSense) holds a plurality market share of the online ad industry? Or that search result ads should be evaluated as their own industry? The first is I believe just not true, and the second seems like an issue of p-hacking your way to a monopoly.
it's usually characterized by a large, but not necessarily majority, market share in a given industry or segment (monopolies can have as little as 30% market share), and pricing power, both of which google has in search.