Retrieve nested MongoDB object after querying nested object

Given the following MongoDB collection groups:

[{
  _id: 'g1',
  name: 'Group 1',
  projects: [{
    _id: 'p1',
    name: 'Project 1',
    tasks: [{
      _id: 't1',
      name: 'Task 1'
    }, {
      _id: 't2',
      name: 'Task 2'
    }]
  }]
}]

I need to find task with _id = t2 and return the whole task object:

{
  _id: 't2',
  name: 'Task 2'
}

I'm able to find the group, either using mongodb:

db.groups.find({ 'projects.tasks._id': ObjectId('t2') })

Or with Mongoose:

Groups.findOne({ 'projects.tasks._id': 't2' })

But of course, this returns the entire group document, and not the task.

I've tried:

db.groups.aggregate([
  {
    $match: { 'projects.tasks._id': ObjectId('t2') }
  }, {
    $replaceRoot: {
      newRoot: '$chapters.sections'
    }
  }
])

But this throws an error.