How to add counter to MongoDB pipeline?

Question

MongoDB

Faced with the task of updating the "order" field in many rows in mongoDB, everything seems to be simple, but I need to insert a number in the "order" field with an iterator step. But I didn’t find anywhere how to set a mutable variable in the pipeline in order to build a function based on it.

There is a set of fields like this:

[
   {"_id": "619ff3d26812666d818a5cd6", "sheet": 46, "order": 32, "name": "Row 1"},
   {"_id": "619ff3d26812666d818a5cd7", "sheet": 46, "order": 1, "name": "Row 2"},
   {"_id": "619ff3d26812666d818a5cd8", "sheet": 46, "order": 23, "name": "Row 3"},
]

I need to update all these fields, with match and sort

db.collection.update({"sheet": 46}, {
   $sort: {
      "name": 1
   },
   $set: {
      "order" : (вот тут мне нужно вставить итератор, который будет увеличиваться на +1 с каждой новой строкой)
   }
})

accumulator will not work here, because. it only works in a group, maybe you can pass it through $function, but how to store the value of the iterator somewhere in a variable, and increase it by +1 every line...

with js and forEach it's not a problem to do this, but I would like to use bson and pipeline for this operation.
if there are connoisseurs of mongoDB, tell me what can be done ...