Changing value in nested array from a scalar to an arry

I need to write a data migration that will convert a field from a scalar value to an array. Some answers I found on line suggest something like:

  [{ $set: { field: ["$field"] } }],
  { multi: true }

but in my case the field is deeply nested in an embedded document + array. How can I traverse the document and then update fields in an array of embedded documents. Structure is something like:

  field_name: {
    prop1: "prop",
      { field: 12 },
      { field: 66 },
and I want to transform those fields to arrays like:
{ field: [12]}
{ field: [66]}

I found that this almost works:

{ $set: { “field_name.nested_array_of_obj.$[].field”: [ “<value of the field???>”]}})
I tried $field_name.nested_array_of_obj.field" or with the [] and it puts that string directly as the value so I get
{ field: [ ‘$field_name.nested_array_of_obj.field’ ]}
{ field: [12] }

Any help would be much appreciated!

Your requirement looks a lot like Mongo query assistance update array element with field from object - #3 by Joshua_D_Souza.

Thanks for the tip.
It is kind of the same, but really my question is about how to reference the value that is based on the field path expression into an array. I would like to know how this works, not just to solve the particular task at hand but also generally understand how the syntax works. Something like:
{ $set: { field: ["$field"] }
works but what happens when field is a more complex path expression into an array like in my example?
{ $set: { "some.nested.$[].array_field": [ <what goes here?> ] }

That is the part @Joshua_D_Souza and I do not know, … yet. I will eventually experiment with $map and $let.

Got some time to

See my answer to equivalent problem at Mongo query assistance update array element with field from object - #5 by steevej

Your problem is even simpler as you do not conditionally map. The following $set and $map should be good:

[ { "$set" :
    { "field_name.nested_array_of_obj" :
      { "$map" :
        { "input" : "$field_name.nested_array_of_obj" ,
          "as" : "item" ,
          "in" : { "field" : [ "$$item.field ] }

@John_Burkhardt1, is your issue resolve? If it is, please mark my post as the solution so that others know that it works. This will help keep this post useful and efficient. It is simply courtesy.