Using MongoDB multikey indexes for covered queries

I have a dynamic schema on MongoDB for different workflow templates. Each workflow template has data attributes associated which is stored as normal <key,value>

[{
  _id : "1",
  team_id : "ABC",
  template_id : "retail_sales",
  document_id : "d1",
  data : [
    { k : "team_id", v : "ABC" },
    { k : "template_id", v : "retail_sales" },
    { k : "recorded_at", v : "2021-10-01T00:00" },
    { k : "billing_state", v : "KA" },
    { k : "pin_code", v : 50001 },
  ]
},
{
  _id : 2
  team_id : "ABC",
  template_id : "simple_crm",
  document_id : "d2",
  data : [
    { k : "team_id", v : "ABC" },
    { k : "template_id", v : "simple_crm" },
    { k : "recorded_at", v : "2021-10-01T00:00" },
    { k : "status", v : "KA" },
    { k : "loan_amount", v : 10000 },
  ]
}]

I have a compound index as follows

{
  team_id : 1,
  template_id : 1,
  document_id : 1,
  "meta.k" : 1, 
  "meta.v" : 1
}

I am looking at optimising my MongoDB aggregation queries and wanted to check how I could have a query with the covered index.

For example, I am looking at the query like below

db.getCollection("<>").aggregate(
    [
        {  
              $match : {
                  "team_id" : "ABC",
                  "template_id" : "retail_sales",
                  data: {
                      $all: [
                          {
                              $elemMatch: {
                                k: "billing_state",
                                v: "KA",
                              },
                          }
                      ]
                   }
                   
              }      
        },
        
        {
            $project: {
                _id: 0,
                "document_id": 1
            },
        },
    ],
    {
        hint : "idx_1"
    }
)

However, the query plan shows that it’s still fetching data and not using the covered index.

Is it possible to query use the covered index where the index is on array of objects?

Additional Details

On looking in to the documentation at https://docs.mongodb.com/manual/core/query-optimization/#std-label-multikey-covering it appears that queries cannot be covered using the multikey indexes.

If multikey indexes cannot be used to cover the query what is the ideal solution to store and query large volume of dynamic data?

May be it is only a redact typo but it looks like there is a mismatch between the index:

and the documents:

The textual explain plan will be much better for us to help you than the nice graphic you posted.