On Wikidata, you can type in a label and autocompletion suggestions appear, similar to the Wikipedia field’s title box:

But you can also paste in a QID and a matching item appears:

Either way, once you select the suggestion, the label ends up in the text box:

Even though Wikidata is built atop QIDs, the QIDs are treated like a machine-readable implementation detail and deemphasized as much as possible in UI.
So I’d suggest rearranging the Identifier, Label, and Description boxes, so that once you select an item, the Label box at the top contains the label, the read-only Description box follows, and the read-only Identifier box contains the QID at the bottom.

This would be particularly good when used for the Architect, Species/Animal, Operator, Network, Brand, Artist, Name Etymology and Subject fields.
So when typing out, for example, in an architect field "Santiago Calatrava", a Wikidata dropdown menu would appear, and upon selection we'd automatically set architect=Santiago Calatrava _and_ wikidata:architect=Q168482.
So when typing out, for example, in an architect field "Santiago Calatrava", a Wikidata dropdown menu would appear, and upon selection we'd automatically set
architect=Santiago Calatrava_and_wikidata:architect=Q168482.
I think people are generally in favor of the idea except for the "automatically" part 👍
@bhousel if we know that the fields architect and wikidata:architect are exact equivalents, what's the risk?
Here’s an example Wikidata API query that would be kicked off after typing in “Junction City” when iD is set to the Vietnamese locale. Notice how the labels and descriptions are in English as a fallback.
Note that this issue is specifically about the behavior of the existing wikidata field type, which is currently only used for the Wikidata field (corresponding to the wikidata tag). #5484 is about adopting that field type for the Operator field (operator:wikidata). I do think this issue would need to be addressed before Wikidata functionality could be added to any other fields, because there isn’t a straightforward mapping from taginfo autocompletion results to Wikidata QIDs.
I did this.

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I did this.