MongoDB: Get count of inner array object with nested array element match

You can do that using MongoDB's aggregation-pipeline :

Different ways to do it, One way is to use $unwind:

Type 1 - Query 1 :

db.collection.aggregate([
    /** Optional but will be good on huge collections to lessen data for further stages */
    {
      $match: { "survey_user.user_option.option_id": "O12" }
    },
    {
      $unwind: "$survey_user"
    },
    /** When you unwind a each object/element in array gets it's own document after `unwind` stage */
    {
      $match: { "survey_user.user_option.option_id": "O12" }
    },
    /** After match you'll only have objects which met the criteria in `survey_user` array */
    /** group on `_id` & push entire original doc to data field */
    {
      $group: { _id: "$_id", survey_user: { $push: "$survey_user" }, data: {  $first: "$$ROOT" } }
    },
    /** Add `survey_user` array to `data.survey_user` & it's size to `data.optedCount` field */
    {
      $addFields: { "data.survey_user": "$survey_user", "data.optedCount": {  $size: "$survey_user" } }
    },
    /** Make `data` as new root to doc */
    {
      $replaceRoot: { newRoot: "$data" }
    }
  ])

Test : mongoplayground

Just in case if you just need count but not needed the entire doc to be returned there will be a minor change in above query :

Type 1 - Query 2 :

db.collection.aggregate([
    {
      $match: { "survey_user.user_option.option_id": "O12" }
    },
    {
      $unwind: "$survey_user"
    },
    {
      $match: { "survey_user.user_option.option_id": "O12" }
    },
    /** Just group on `_id` & count no.of docs, maintain `survey_id` */
    {
      $group: { _id: "$_id", optedCount: { $sum: 1 }, survey_id: { $first: "$survey_id" } }
    }
  ])

Test : mongoplayground

Using array iterator $reduce, which might be helpful if your collections data is so huge, as unwind will explode your docs.

Type 2 - Query :

db.collection.aggregate([
  {
    $match: {
      "survey_user.user_option.option_id": "O12",
    },
  },
  /** Instead of `$addFields`, you can use `$project` to project fewer needed fields (which can be help improve query with performance benefits ) */
  {
    $addFields: {
      optedCount: {
        $reduce: {
          input: "$survey_user",
          initialValue: 0,
          in: {
            $cond: [
              { $in: ["O12", "$$this.user_option.option_id"] },
              { $add: ["$$value", 1] },
              "$$value",
            ]
          }
        }
      }
    }
  }
]);

Test : mongoplayground