But if we use a broader definition, basically "a formal language that specifies behavior a machine must execute", then HTML is indeed a programming language.
HTML is not only about annotating documents or formatting, it can do things you expect from a "normal" programming language too, for example, you can do constraints validation:
<input name="token" required pattern="[A-Z]{3}-\d{4}" title="Must match ABC-1234 (3 uppercase letters, hyphen, 4 digits)" placeholder="ABC-1234">
That's neither annotating, just a "document" or just formatting. Another example is using <details> + <summary> and you have users mutating state that reveals different branches in the page, all just using HTML and nothing else.In the end, I agree with you, HTML ultimately is a markup language, but it's deceiving, because it does more than just markup.