Convert object property to array with one element per key

I am trying to use Jolt to transform an object into an array with one array element per key in the original object. I'd like the output objects to include the original key as a property, and preserve any properties from the source value. And I need to handle three scenarios for the input properties:

• "key": null
• "key": {}
• "key": {...}

Here's an example:

{
  "operations": {
    "foo": null,
    "bar": {},
    "baz": {
      "arbitrary": 1
    }
  }
}

And the desired output"

{
  "operations": [
    {
      "operation": "foo"
    },
    {
      "operation": "bar"
    },
    {
      "operation": "baz",
      "arbitrary": 1
    }
  ]
}

Note: foo, bar and baz are arbitrary here. It needs to handle any property names inside the operations object.

This is really close to what I want:

[
  {
    "operation": "default",
    "spec": {
      "operations": {
        "*": {}
      }
    }
  },
  {
    "operation": "shift",
    "spec": {
      "operations": {
        "*": {
          "$": "operations[].operation"
        }
      }
    }
  }
]

But it drops "arbitrary": 1 from the baz operation.

Alternately this keeps the properties in the operations, but doesn't add a key for the operation name:

[
  {
    "operation": "default",
    "spec": {
      "operations": {
        "*": {}
      }
    }
  },
  {
    "operation": "shift",
    "spec": {
      "operations": {
        "*": {
          "@": "operations[]"
        }
      }
    }
  }
]

Any help getting both behaviors would be appreciated.