OpenAPI definition does not include child objects in doc JSON

Question

I am in the process of taking a look into polymorphism for OpenAPI. More specifically I am in trying out the example with the Pet, Cat and Dog found here using this portion of yaml:

components:
  schemas:
    Pet:
      type: object
      discriminator:
        propertyName: petType
      properties:
        name:
          type: string
        petType:
          type: string
      required:
      - name
      - petType
    Cat:  ## "Cat" will be used as the discriminator value
      description: A representation of a cat
      allOf:
      - $ref: '#/components/schemas/Pet'
      - type: object
        properties:
          huntingSkill:
            type: string
            description: The measured skill for hunting
            enum:
            - clueless
            - lazy
            - adventurous
            - aggressive
        required:
        - huntingSkill
    Dog:  ## "Dog" will be used as the discriminator value
      description: A representation of a dog
      allOf:
      - $ref: '#/components/schemas/Pet'
      - type: object
        properties:
          packSize:
            type: integer
            format: int32
            description: the size of the pack the dog is from
            default: 0
            minimum: 0
        required:
        - packSize

Using this I am able to create the DTOs using the OpenAPI spring generator correctly and with a proper structure. Now all seem fine up to this step but when I serve the SwaggerUI using the Spring's dependencies the generated subclasses are not served as part of the schema. For instance, when I fetch the JSON definition of this I get the following:

{
    "openapi": "3.0.1",
    "info": {
        "title": "OpenAPI definition",
        "version": "v0"
    },
    "servers": [{
        "url": "http://localhost:8080",
        "description": "Generated server url"
    }],
    "tags": [{
        "name": "Test",
        "description": "the Test API"
    }],
    "paths": {
        "/test": {
            "get": {
                "tags": ["Test"],
                "operationId": "testGet",
                "responses": {
                    "200": {
                        "description": "A list of search results",
                        "content": {
                            "application/json": {
                                "schema": {
                                    "$ref": "#/components/schemas/Pet"
                                }
                            }
                        }
                    }
                }
            }
        }
    },
    "components": {
        "schemas": {
            "Pet": {
                "required": ["name", "petType"],
                "type": "object",
                "properties": {
                    "name": {
                        "type": "string"
                    },
                    "petType": {
                        "type": "string"
                    }
                },
                "discriminator": {
                    "propertyName": "petType"
                }
            }
        }
    }
}

As we can see there is no Cat or Dog definition. This in turn makes consumers of this JSON definition to incorrectly generate their code.

My question is thus, what needs to be done in order to get this working properly. For reference I am using OpenAPI 3.0.1, SpringBoot 3.0 and the following swagger and springdoc dependencies:

implementation 'org.openapitools:jackson-databind-nullable:0.2.4'
implementation 'io.swagger.core.v3:swagger-annotations:2.2.7'
implementation 'org.springdoc:springdoc-openapi-starter-webmvc-ui:2.0.0'