Retrieve Wikimedia Commons Category of a Wikipedia page using the Wikimedia API

I am trying to use the Wikimedia Api to get the corresponding Wikimedia Commons category to a specific Wikipedia page. I assume that it is possible as most Wikipedia pages include an "in other projects" - section in the sidebar which has a link that redirects to the Commons Category (for example: https://de.wikipedia.org/wiki/Albert_Einstein)

Thanks in advance.

You can do it in two API calls, the first call to German Wikipedia gets you the Wikidata Qid:

https://de.wikipedia.org/w/api.php?action=query&format=json&prop=wbentityusage&titles=Albert%20Einstein&wbeuprop=&wbeuaspect=

Which returns:

{
    "batchcomplete": "",
    "query": {
        "pages": {
            "1278360": {
                "pageid": 1278360,
                "ns": 0,
                "title": "Albert Einstein",
                "wbentityusage": {
                    "Q937": {
                        "aspects": [
                            "S",
                            "T",
                            "C.P227",
                            "C.P214",
                            "C.P244"
                        ]
                    }
                }
            }
        }
    }
}

Then you can use the Wikidata API to get the name of the Commons category: https://www.wikidata.org/w/api.php?action=wbgetclaims&format=json&entity=Q937&property=P373

Which returns:

{
    "claims": {
        "P373": [
            {
                "mainsnak": {
                    "snaktype": "value",
                    "property": "P373",
                    "hash": "be154a8a3dfc826844ceb5a62389857a65ff1e4e",
                    "datavalue": {
                        "value": "Albert Einstein",
                        "type": "string"
                    },
                    "datatype": "string"
                },
                "type": "statement",
                "id": "q937$2F332903-133D-4CA0-AD24-8B4292C2BF89",
                "rank": "normal"
            }
        ]
    }
}

The value in datavalue is the name of the category. You get the full URL by just prepending https://commons.wikimedia.org/wiki/Category:

https://commons.wikimedia.org/wiki/Category:Albert Einstein