I wonder why no one so far has created a gadget to show these descriptions in desktop articles. Seems pretty easy to do and will allow people to experiment before including it into the core software.

I have!
mw.loader.load('/w/index.php?title=User:Jdlrobson/wikidataInfobox.js&action=raw&ctype=text/javascript');

(although apparently it only works on the mobile skin now.. but easily fixable)

@Jdlrobson: How is T141230 (for mobile web) a duplicate of this task (for desktop)?

Just a note that I removed the Wikidata edits in watchlist part because I just didnt have the right setting enabled; I misunderstood, and have it set up properly to show wikidata edits in watchlist now.

Thanks @Samwalton9 for your feedback. To confirm this is not about showing Wikidata edits in Wikipedia? Feel free to remove that possible solution from the description if I've misrepresented it and it's not relevant!

My note was that one possible solution would be for Wikidata edits to show up in Wikipedia watchlists for watched pages, because I thought that feature didn't exist, but it turns out it does.

Is this still stalled Olga now they can be overridden? Does this mean we can add them back on English?

In T161596#4183011, @Jdlrobson wrote:

Is this still stalled Olga now they can be overridden? Does this mean we can add them back on English?

I think stalled is still appropriate. Even with the magic word, I think the conversation so far on keeping the descriptions has only revolved around the apps. We'd probably have to do another round of community consultation before looking at this again.

@ovasileva: If I understand the last comment correctly, this is "only" blocked on having consultations? If there is no (sub)task for such a consultation itself and no other technical blockers blocking this very task, then this task should likely be open with lowest priority, as stalled status means waiting for further input (e.g. from its reporter or a third party) and can currently not be acted on, or declined. Thanks.