Semantic HTML was already fashionable in late 2004, when I was a graphic designer arguing against table tags. But my own exposure is a bad measure, just as is anyone else's. One of the most famous groups pushing for well-written HTML was WaSP, and it turns out that it was founded in 1998, https://en.wikipedia.org/wiki/Web_Standards_Project
This article is from 2008, but I think it would be quite challenging to find something similar from 1999.