Adding a $match query with mongodb lookup

I am pulling data from 2 collections as shown in this MongoDB playground. While pulling the data from the second collection, I want to create a match on tag, such that only those posts are returned that have the particular tag associated with them.

Here is the query that I created:

db.Vote.aggregate([
    {
        $match: {
            comment: {
                $ne: null,
            },
            "comment.topic": {
                $exists: 1,
                $regex: ".",
                $options: "i",
            },
        },
    },
    {
        $group: {
            _id: {
                topic: "$comment.topic",
                text_sentiment: "$comment.text_sentiment",
            },
            total: {
                $sum: 1,
            },
            postIds: {
                $push: "$postId",
            },
        },
    },
    {
        $group: {
            _id: "$_id.topic",
            total: {
                $sum: "$total",
            },
            text_sentiments: {
                $push: {
                    k: "$_id.text_sentiment",
                    v: "$total",
                },
            },
            postIds: {
                $push: "$postIds",
            },
        },
    },
    {
        $project: {
            topic: "$_id",
            topicOccurance: "$total",
            sentiment: {
                $arrayToObject: "$text_sentiments",
            },
            postIds: {
                $reduce: {
                    input: "$postIds",
                    initialValue: [],
                    in: {
                        $concatArrays: ["$$value", "$$this"],
                    },
                },
            },
        },
    },
    {
        $sort: {
            topicOccurance: -1,
        },
    },
    {
        $lookup: {
            from: "Post",
            localField: "postIds",
            foreignField: "_id",
            as: "tag",
        },
    },
    {
        $addFields: {
            postIds: {
                $setUnion: "$postIds",
            },
            tag: {
                $setUnion: {
                    $map: {
                        input: "$tag",
                        in: "$$this.tag",
                    },
                },
            },
        },
    },
]);

The result looks similar to:

{
    "_id" : "Collaboration & Teamwork",
    "topic" : "Collaboration & Teamwork",
    "topicOccurance" : 355,
    "sentiment" : {
        "Negative" : 102,
        "Neutral" : 132,
        "Positive" : 121
    },
    "postIds" : [
        "0iWc2U8FVz",
        "3Qzysi2cXD",
        "3hRx7qAvcb",
        "BsrTDkHmkE",
        "LT2HE2uEa5",
        "Qw0WcUBcnY",
        "U72zss2Af5",
        "V9DcRcSawi",
        "hNwFVJ2bBk"
    ],
    "tag" : [
        [
            "Engagement"
        ],
        [
            "Environment"
        ],
        [
            "Feedback & Recognition"
        ],
        [
            "Leadership"
        ],
        [
            "Management"
        ],
        [
            "Meaningful Work"
        ],
        [
            "Open Text"
        ]
    ],
    "totalDocs" : 39
}

After the tag match, the response will only have Posts that have tag = foo. How can I do that?

Mongo DB Playground : This has the above query with the sample data.