What does it mean: "On a page that is connected to a Wikidata item via the interwiki links, you can use the function by adding the label of the property you want in your language or the P-number of the property. The code has to be added in the wikicode.
{{#statements:member of political party}} or {{#statements:P102}} will return the "member of political party" value.
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As far as I understood interwiki links are simply a special kind of link, they don't act on page level and they don't modify the behaviour of the page.
https://www.wikidata.org/wiki/Wikidata:How_to_use_data_on_Wikimedia_projects#Direct_access
Every Wikipedia article can be connected to a Wikidata item. Interwiki links these days are mostly automatically generated between articles in different languages connected to the same Wikidata item. {{#statements}} and similar functions pull information from the connected Wikidata item.
Non-Wikimedia wikis do not have similar features currently; Wikidata integration requires direct database access.