There's nothing intrinsic about Google search that makes it a monopoly. Monopolies usually hold their position because regulations make it prohibitive for competitors to form or because they control a rare resource. Google search does neither of these two things. Its just a better product compared to everything else out there and the market reflects that.
You forgot to exclude the "not usual" factors that allow monopolies to hold their position to rule Google out of the group.
For example, non-regulatory attempts at blocking of competitors, which Google does engage in due to their dominant position in mobile (of course, that's also just another better product)
Monopolies hold because companies engage in foul play to hold their monopolies. When Google goes out and pays Apple billions to default to Google Search, that is not a regulatory hurdle, nor is Google using its position as the Android platform maintainer and bundling Google Search with Play Services.
The query logs and “permission” to crawl are both advantages vs startups.
You can't legally make a crawler to compete with Google anymore, it's explicitly stated in a lot of robots.txt's.
A rational take, prepare to get downvoted to oblivion!
Do they control the Trademark "Google"? Do they control the Domain Name "Google.com"?
Do they control the default Search engine for Android? For Chrome?
Did they pay to be the default Search engine on iPhone? On Firefox?
Are those rare resources? I'd say yes.
And you're conflating "illegally-maintained Monopoly" with "Monopoly." Whether they got there through using illegal tactics or not is a separate question from whether they are a Monopoly now. 90% - is that a high enough market share to qualify as a monopoly, when their annual revenue is like $224 billion? What percentage would be enough to convince you? Does it need to be 100%?