How to emulate a subquery and remove value from an array

I’m attempting to remove the stringified ID from a document in one collection from an any arrays in another collection in mongosh. Below is a full script to execute the attempt.

It seems to be working up until I try to access the value in the returned object.

db.collection1.drop();
db.createCollection("collection1");
db.collection1.insertMany(
    [
        {_id: ObjectId("66477b28bf237b16b21a55b6"), value: "value1"},
        {_id: ObjectId("66477b28bf237b16b21a55b7"), value: "value2"},
        {_id: ObjectId("66477b28bf237b16b21a55b8"), value: "value3"},
        {_id: ObjectId("66477b28bf237b16b21a55b9"), value: "value4"}
    ]
);
db.collection2.drop();
db.createCollection("collection2");
db.collection2.insertMany([
    {name: "name1", values: ["66477b28bf237b16b21a55b6", "66477b28bf237b16b21a55b7"]},
    {name: "name2", values: ["66477b28bf237b16b21a55b6", "66477b28bf237b16b21a55b8"]},
    {name: "name3", values: ["66477b28bf237b16b21a55b7", "66477b28bf237b16b21a55b9"]},
    {name: "name4", values: ["66477b28bf237b16b21a55b8", "66477b28bf237b16b21a55b9"]}
]);

// 
let valueId = db.collection1.aggregate([
    {$match: {value: "value4"}},
    {$project: {idString: {"$toString": "$_id"}}}
]);
print(valueId);
// The print statement above shows:
//{
//  _id: ObjectId('66477b28bf237b16b21a55b9'),
//  idString: '66477b28bf237b16b21a55b9'
//}

// This works:
//db.collection2.updateMany({}, {
//        $pull: { values: "66477b28bf237b16b21a55b9" }
//    }
//);

// This does not:
db.collection2.updateMany({}, {
        $pull: { values: valueId.idString }
    }
);

I’m out of town and unable to check it for the next week or so.

I’ll respond properly when I can test it.