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.

"Search" is a borderline obsolete concept. There is no separation between search, AI, information retrieval, knowledge synthesis, information tasks, etc.