How to set data in custom option filed which is created progrmatically in Magneto 2

I have created a custom field “Plan Identifier” in custom option for products.

Now, I want this field to be updated when we create a product using REST API and also the data of this filed when we make a GET request.
I tried to send this in the payload:

{
  "product": {
    "sku": "prod-111",
    "name": "abcd", 
    "attribute_set_id": 4,
    "price" : 400,
    
    "options": [
        {
            "product_sku": "prod-111",
            "title": "Rental Plan",
            "type":"drop_down",
            "plan_identifier": "some Data",
            "is_require" : true,
            "sort_order" : 4,
            "values": [
                {
                    "title": "Half Day Plan",
                    "price": 0,
                    "price_type" : "fixed",
                    "sku": "drop_down option 1 sku",
                    "sort_order": 1
                },
                {
                    "title": "Full Day Plan",
                    "price": 50,
                    "price_type" : "fixed",
                    "sku": "drop_down option 1 sku 1",
                    "sort_order": 2
                }
            ],
            "extension_attributes": {
                "plan_identifier": "new data"
            }
        }
    ]
}
}

Then I created a beforeSave plugin to save this data. I tried using extension attribute too but nothing works. Here is the error I am getting:

"message": "Property "PlanIdentifier" does not have accessor method "getPlanIdentifier" in class "Magento\Catalog\Api\Data\ProductCustomOptionExtensionInterface".",

Please suggest the correct way of doing it and help me.