If all you're doing is using HTML to "annotate a document with its structure and its formatting", then yes, I'll accept that it's not quite programming, but I've not seen this approach of starting with a plain non-html document and marking it up by hand done in probably over two decades. I do still occasionally see it done for marking up blog posts or documentation into markdown and then generating html from it, but even that's a minuscule part of what HTML is used for these days.
Your mileage my vary, but what I and people around me typically do is work on hundreds/thousands of loosely coupled small snippets of HTML used within e.g. React JSX, or Django/Jinja templates or htmx endpoints, in order to dynamically control data and state in a large program. In this sense, while the html itself doesn't have control flow, it is an integral part of control flow in the larger system, and it's extremely likely that I'll break something in the functionality if I carelessly change an element's type or attribute value. In this sense, I'm not putting on a different hat when I'm working on the html, but just working on a different part of the program.