PHP updating multiple elements of sub-array of MongoDB document

I have the following document structure. I am trying to update specific values inside the holes sub-array:

Each holes Array element is an Object representing the score on a golf hole, with various properties (fields). I am trying to provide the ability to update the holeGross field ONLY for each score. On my PHP website, this is using a POST form, which pushes an Array of scores and the round._id value too, as:

Array ( [holeScoreHidden] => Array ( [1] => 7 [2] => 7 [3] => 7 [4] => 8 [5] => 7 [6] => 7 [7] => 7 [8] => 7 [9] => 7 ) [roundId] => 60c642db09080f1b50331b2d [submit] => )

I have had some assistance on the MongoDB forums, with MongoDB-native (i.e. shell) syntax which I have tested in Compass and works:

[{$match: {
  _id: ObjectId('60c916684bd16901f36efb3a')
}}, {$set: {
  holes: {
    $map: {
      input: { $range: [0, { $size: "$holes"}]},
      in: {
        $mergeObjects: [
            { $arrayElemAt: ["$holes", "$$this"] },
            { holeGross: { $arrayElemAt: [[9,8,7,6,5,4,3,2,1], "$$this"] } }
          ]
      }
    }
  }
}}]

Using this as a basis, I tried converting to PHP-equivalent, as follows:

function setRoundScores($roundId, $scoresArray) {
        
    $collection = $client->golf->roundTest;
        
    $match = [ '_id' => new MongoDB\BSON\ObjectID( $roundId ) ];
        
    $set = [
        '$set' => [
            'holes' => [
                '$map' => [
                    'input' => [
                        '$range' => [ 0, [ '$size' => '$holes']],
                        'in' => [
                            '$mergeObjects' => [
                                [ '$arrayElemAt' => [ '$holes', '$$this' ]],
                                [ 'holeGross' => [ '$arrayElemAt' => $scoresArray, '$$this' ]]
                            ]
                        ]
                    ]
                ]
            ]
        ]
    ];
        
    $updateOne = $collection->updateOne($match,$set);
        
    return $updateOne->getUpsertedId();
        
}

But this errors with:

Fatal error: Uncaught MongoDB\Driver\Exception\BulkWriteException: The dollar ($) prefixed field '$map' in 'holes.$map' is not valid for storage. in /var/www/html/vendor/mongodb/mongodb/src/Operation/Update.php:228 Stack trace: #0 /var/www/html/vendor/mongodb/mongodb/src/Operation/Update.php(228): MongoDB\Driver\Server->executeBulkWrite('golf.roundTest', Object(MongoDB\Driver\BulkWrite), Array) #1 /var/www/html/vendor/mongodb/mongodb/src/Operation/UpdateOne.php(117): MongoDB\Operation\Update->execute(Object(MongoDB\Driver\Server)) #2 /var/www/html/vendor/mongodb/mongodb/src/Collection.php(1075): MongoDB\Operation\UpdateOne->execute(Object(MongoDB\Driver\Server)) #3 /var/www/html/functions.php(803): MongoDB\Collection->updateOne(Array, Array) #4 /var/www/html/updateRound.php(19): setRoundScores('60cb07d14bd1690...', Array) #5 {main} thrown in /var/www/html/vendor/mongodb/mongodb/src/Operation/Update.php on line 228

I am getting very confused as to the equivalent syntax, or even if the same methods are available in the PHP driver?

Can anyone point out the syntax issues / errors?

Finally, could I simply replace the entire holes sub-array, and provide that as a whole var to the updateOne() call? This would send much more data and is not the most efficient obviously...

*** UPDATE ***

@Joe was of great help in the final answer. @Joe provided a single line covering what was the cause of the issue.

For posterity, I thought to repost the final syntax of my function for others to be able to follow:

function setRoundScores($roundId, $scoresArray) {
        
    $client = new MongoDB\Client($_ENV['MDB_CLIENT');

    $collection = $client->golf->round;

    $match = [ '_id' => new MongoDB\BSON\ObjectID( $roundId ) ];
        
    $set = [
        '$set' => [
            'holes' => [
                '$map' => [
                    'input' => [
                        '$range' => [ 0, [ '$size' => '$holes']]
                    ],
                    'in' => [
                        '$mergeObjects' => [
                            [ '$arrayElemAt' => [ '$holes', '$$this' ]],
                            [ 'holeGross' => [ '$toInt' => [ '$arrayElemAt' => [ $scoresArray, '$$this' ]]]]
                        ]
                    ]
                        
                ]
            ]
        ]
    ];
        
    $updateOne = $collection->updateOne($match, [$set]);
        
    return $updateOne->getModifiedCount();
        
}

Of note, also needed to cast the $_POST array's fields to Int's as they are converted to Strings, so using the '$toInt' method to perform this on the DB as well. Lots of extra square braces...

Also this is not an upsert so just returning the modified count instead.