How to conditional update a field in aggregtion if field with certain value exists in array?

How can I use aggregate to update a field if a field with value exists in an array?

orders: [
    { id: 100, status: "shipped", options: [{ returned: true }] },
    { id: 101, status: "packed", options: [{ quick: true }] },
    { id: 102, status: "ordered" }
]

desired result: [
    { id: 100, status: "returned", options: [{ returned: true }] }, // <- updated status
    { id: 101, status: "packed", options: [{ quick: true }] },
    { id: 102, status: "ordered" }
]

I can set an additional field, but I have not managed a conditional update, tried with $set and $cond but it would not work together.

$set {
  status: { options: {$elemMatch: {returned: true}}}
}

MongoDB Playground

Thanks,
bluepuma

How to move from array to field:

db.orders.aggregate([
  {
    $set: {
      returned: "$options.returned"
    }
  },
  {
    $unwind: {
      path: "$returned",
      preserveNullAndEmptyArrays: true
    }
  }
])

But how can I update the status field if returned: true?

The $unwind to get the additional field sounds expensive, I tried to use project:

$project: {
    returned: { 
        $cond: [
            { $eq: [ '$options.returned', true ] }, 
            true, 
            false
        ]
    }
}

But that gives me an error Invalid $project :: caused by :: Cannot use expression other than $meta in exclusion projection.