There should be some way to get information which Wikidata id:s exists in Kartographer (see also T155925). For my purpose (which is using the information to detect which Wikidata pages have OSM wikidata tags) daily CSV export of existing ids to public web server with following information would be enough:
- Wikidata id (value of the OSM wikidata-tag)
- OSM relation id
- OSM name if there is any
- lat, lon
optionally all other OSM tags would be useful too.
Pulling this kind of information directly from OSM seems to be hard because loading all items with Wikidata ids with Overpass is not possible (least not without multiple queries) because generated dataset is too big.