MongoDB 聚合 groupBy 日期并计算子文档

我知道这里有这个问题的其他版本，但我正在努力让这个问题保持一致.我有类似以下内容的文档:

[
{_id: 1, date: "2022-04-08T23:30:12.000Z", books: [{author: "Johnson", title: "First Title"}, {author: "Smith", title: "Second Title}]},
{_id: 2, date: "2022-04-22T23:30:12.000Z", books: [{author: "Johnson", title: "Some Other Title"}]},
{_id: 3, date: "2022-05-05T23:30:12.000Z", books: [{author: "Smith", title: "Title Round 2"}]},
{_id: 4, date: "2022-05-15T23:30:12.000Z", books: [{author: "Johnson", title: "Found a Title", {author: "Smith", title: "Wrote again"}, {author: "Brooks", title: "New Title"}]}
]

我try 按月-年对文档进行分组，然后计算不同值显示在作者字段上的次数.到目前为止，我有一个管道，看起来像:

{
          "$unwind": "$books"
        },
        {
          $project: {
            _id: 1,
            books: 1,
            month: {
              "$month": "$date"
            },
            year: {
              "$year": "$date"
            }
          }
        },
        {
          $project: {
            _id: 1,
            books: 1,
            date: {
              $concat: [
                {
                  $substr: [
                    "$year",
                    0,
                    4
                  ]
                },
                "-",
                {
                  $substr: [
                    "$month",
                    0,
                    2
                  ]
                },
                
              ]
            }
          }
        },
        {
          $group: {
            _id: {
              date: "$date",
              books: {
                freq: {
                  $sum: 1
                }
              }
            }
          }
        },
        {
          $project: {
            "_id": 1,
            "date": 1,
            "books": 1
          }
        },
        
      ]
    }

我的目标是最终输出如下所示:

[
{date: "2022-04", authors: { "Johnson": 2, "Smith": 1}},
{date: "2022-05", authors: {"Johnson": 1, "Smith": 2, "Brooks": 1}}
]

我已经找到了对子文档运行计数的方法，但在try 实现时，我正在丢失按日期分组的方法，或者只是得到错误.我已经看得够多了，知道它是可行的，只是在试图把它做得恰到好处时迷失了方向.如有任何帮助，我们不胜感激.