Mongodb $elemMatch within $addElement

Working with Data
#1

I have a set of documents as below:

    PropName: 'abc',
    TrDates:[{TrDate:367334},{TrDate:367444}]
    
    PropName: 'pqr',
    TrDates:[{TrDate:367540},{TrDate:367655}]
    
    PropName: 'xyz',
    TrDates:[{TrDate:367550},{TrDate:367650}]

To filter records having at least one element of the TrDates falling into a given rage, I wrote the following in the $match stage of aggregate pipeline which works fine:

 [$match: {
      TrDates: {
        $elemMatch: {
          TrDate: {
            $gte: 367400,
            $lte: 367600
          }
        }
      } 
    }]

Now I have another requirement to add a new field based on the same condition, i.e: add WithinRange: true to the documents meeting the same condition as above; something like this:

$addFields:{
  WithinRange: {$cond: [ { $and: [{$gte: [ "$TrDates.TrDate", 367400 ]}, {$lte: [ "$TrDates.TrDate", 367600 ]}]}, true, false ]}
}

But this doesn’t work. I can use $filter combined with array size checking, but doubt the efficiency. Also I read $elemMatch can be used only within the $match. If that’s the case what’s the most efficient way to do this query?