Working with Subdocument arrays and document references

Working with Data Node.js Frameworks
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Hey all, I am pretty new to mongodb but I wanted to use it for my first mern stack project. I am using mongoose with nodejs. I currently have 3 schema’s, Year at the topmost level, then a year has a subdocument array of 12months, and then each month has a reference to an envelope.

const yearSchema = new mongoose.Schema({
  year: {
    type: Number,
    required: true,
    unique: true,
  },
  budgetTotal: {
    type: Number,
    default: 0,
  },
  months: [month.schema],
});

const monthSchema = new mongoose.Schema({
  month: {
    required: true,
    type: String,
  },
  total: {
    default: 0,
    type: Number
  },
  envelopes: [{
    type: mongoose.Schema.Types.ObjectId,
    ref: "Envelope",
  }],
});

const envelopeSchema = new mongoose.Schema({
  month: {
    type: mongoose.Schema.Types.ObjectId,
    ref: "Month",
    required: true,
  },
  category: {
    required: true,
    type: String
  },
  budget: {
    required: true,
    type: Number
  }
});

I am struggling to work with the data. I can do get requests easy enough to find the document from a specific year. I can also post a new year and delete the whole year. What I can’t figure out how to do is modify the embedded elements. I’ve spent this morning trying to get a year then update the total parameter for each value in the month. This doesn’t work,

const data = await Year.updateMany({ year: Number(req.params.year) }, { $inc: { "months.$.total": 500 } });

my error from it was

"message": "The positional operator did not find the match needed from the query."

I also don’t understand how I would create a new envelope and make sure it’s associated with the month. I would appreciate any tips/pointers to working with data like this. I really want to get a better understanding of working with mongo