About 10 or 12 years ago when learning HTML5 (which was new at that time!), I remember there were a lot of discussions about the Document Outline and how the new HTML elements will improve accessibility and the browsing experience.
Looking at the web today, I’m wondering where all of this went? Is the Document Outline a thing people care about? Should I care about it?
I think you are referring to the Document Outline Algorithm, which basically allowed the browser to recalculate the heading levels so that they made sense. This outline was actually defined in the WHATWG HTML specification for many years until recently. It has now been removed and there officially exists no such algorithm.
The truth is that even though the document outline algorithm was defined in the spec for years, no browser ever implemented it. So really, it only existed on paper. You could never rely on it in practice. And that’s the primary reason why it has been officially removed from the spec.
So in answer to your question, no, it is not something people care about and you should not care about it because it is not a thing that was ever implemented in any browser and it is no longer in the official specs.