Earlier quoted context omitted.
There is a tool to get infobox data from Wikipedia into Wikidata: https://pltools.toolforge.org/harvesttemplates/ The easily parsable Infobox data can probably already be found in Wikidata (assuming there is a property).
So am I right in thinking Wikidata is sort of scraped from Wikipedia internally? The other way round seems better, but obviously too late.
Some wikipedia infoxes are based on wikidata. I can't find an example, but here some links:
* https://commons.wikimedia.org/wiki/Commons:Wikidata_infobox_...
* https://commons.wikimedia.org/wiki/Template:Wikidata_Infobox
* https://en.wikipedia.org/wiki/Template:Infobox_person/Wikida...
There are lexeme too, and it is not based on wiktionary. Search the prefix "L:" (without quote).
Example:
* https://www.wikidata.org/w/index.php?search=L%3Acat&search=L...
* https://www.wikidata.org/wiki/Lexeme:L7
Also, there are a lot of tools on toolforge.org. One is reasonator which produce sentences from a wikidata item: https://reasonator.toolforge.org/?q=Q1339