There is definitely a grey area, but HTML is pretty far away from it. HTML doesn't "execute" and is very far from Turing completeness. You cannot write programs in it, and that is the key. Pure HTML is very much on the side of "rendering text" and not "running software." Once we start talking about things like LaTex though, the line gets a lot harder to see. Note that whether HTML is "code" is irrelevant. The point is that whether it's "code" or not, it is never a program.
Edit: typo in "grey"
They also contract a company that trains facial recognition AI on social media. I think the Real ID is the least if most people's worries