Update element matching specific value in an array

Question

I have a collection product. In this collection for all document I have an array refs_fr with an unknown number of elements:

refs_fr :
   [{
      "typ": "string_a"
      "id": "string_a"
      "url": "string_a"
      "exp": "
    },     
    {
      "typ": "string_b"
      "id": "string_b"
      "url": "string_b"
      "exp": "string_b"
     },
     {
      ...
     },
     ...
    ]

My goal is to update element in ref_fr of each documents where fields of the element match a specific value.

Currently my code look like this :

        updates = {
            "refs_fr.id": ref["newID"],
            "refs_fr.typ": ref["newType"],
            "refs_fr.url": ref["newURL"],
            "refs_fr.exp": ref["newExp"]
        }
        await db.collection.update_many({"refs_fr.[]": { "$elemMatch": {"id": ref["id"]}}}, {"$set": { "refs_fr."updates} })

It doesn't update my documents, I saw that I should use $[<identifier>] but I struggle with the syntax. Anyone can help me on this point?

Thanks in advance!