TfD sections are actually h4, but I agree that this would be very useful and much needed as subscribing to the h2 on these pages just isn't a valid option.

Just to repeat myself, again, mw.wikibase is completely irrelevant to this, as is Wikidata. I'm not trying to access the description at Wikidata, for that I can use mw.wikibase.getDescription, which is already available. I'm trying to access the local description which can be seen either on the article itself, or in the "Page information" page. That can give a completely different description.

Just to be clear, I'm not trying to get the description located at wikidata, but the one at the local wiki. See this page information "Local description" section.

I mean short description, the line of text that is associated with a page in search results and other places. I have no idea what TextExtracts, but looking at its documentation, it doesn't seem to be what I'm asking for.