I just ran the same test on Gemini 2.5 pro (I assume it enables search by default, because it added a bunch of "sources") and got the exact same result as the author. It claims ".bdi" is the ccTLD for Burundi, which is false they have .bi[1]. It claims ".time" and ".article" are TLDs.
I think the authors point stands.
EDIT: I tried it with "Deep Research" too. Here it doesn't invent either TLDs or HTML Element, but the resulting list is incomplete.