When I studied at University 15 years ago web 2.0 was in full swing and the academics where busy talking about web 3.0 which was at the time understood as "the semantic web".
Web 3.0 I have a soft spot for. It was a stupid name and the ideas didn’t really work but the semantic web people had their hearts in the right place.
Nobody said "web2", indeed, but that doesn't invalidate that Web 2.0 described a very distinct and substantial evolution of what is possible in the browser.