feat(responses)!: introduce OpenAI compatible prompts to Responses API (#3942)

# What does this PR do?
<!-- Provide a short summary of what this PR does and why. Link to
relevant issues if applicable. -->
This PR is responsible for making changes to Responses API scheme to
introduce OpenAI compatible prompts there. Change to the API only,
therefore currently no implementation at all. However, the follow up PR
with actual implementation will be submitted after current PR lands.

The need of this functionality was initiated in #3514. 

> Note, #3514 is divided on three separate PRs. Current PR is the second
of three.

<!-- If resolving an issue, uncomment and update the line below -->
<!-- Closes #[issue-number] -->

## Test Plan
<!-- Describe the tests you ran to verify your changes with result
summaries. *Provide clear instructions so the plan can be easily
re-executed.* -->
CI

docs/static/deprecated-llama-stack-spec.yaml

@@ -6402,11 +6402,44 @@ components:
       oneOf:
         - $ref: '#/components/schemas/OpenAIResponseInputMessageContentText'
         - $ref: '#/components/schemas/OpenAIResponseInputMessageContentImage'
+        - $ref: '#/components/schemas/OpenAIResponseInputMessageContentFile'
       discriminator:
         propertyName: type
         mapping:
           input_text: '#/components/schemas/OpenAIResponseInputMessageContentText'
           input_image: '#/components/schemas/OpenAIResponseInputMessageContentImage'
+          input_file: '#/components/schemas/OpenAIResponseInputMessageContentFile'
+    OpenAIResponseInputMessageContentFile:
+      type: object
+      properties:
+        type:
+          type: string
+          const: input_file
+          default: input_file
+          description: >-
+            The type of the input item. Always `input_file`.
+        file_data:
+          type: string
+          description: >-
+            The data of the file to be sent to the model.
+        file_id:
+          type: string
+          description: >-
+            (Optional) The ID of the file to be sent to the model.
+        file_url:
+          type: string
+          description: >-
+            The URL of the file to be sent to the model.
+        filename:
+          type: string
+          description: >-
+            The name of the file to be sent to the model.
+      additionalProperties: false
+      required:
+        - type
+      title: OpenAIResponseInputMessageContentFile
+      description: >-
+        File content for input messages in OpenAI response format.
     OpenAIResponseInputMessageContentImage:
       type: object
       properties:
@@ -6427,6 +6460,10 @@ components:
           default: input_image
           description: >-
             Content type identifier, always "input_image"
+        file_id:
+          type: string
+          description: >-
+            (Optional) The ID of the file to be sent to the model.
         image_url:
           type: string
           description: (Optional) URL of the image content
@@ -6697,6 +6734,10 @@ components:
           type: string
           description: >-
             (Optional) ID of the previous response in a conversation
+        prompt:
+          $ref: '#/components/schemas/OpenAIResponsePrompt'
+          description: >-
+            (Optional) Reference to a prompt template and its variables.
         status:
           type: string
           description: >-
@@ -7036,6 +7077,30 @@ components:
         OpenAIResponseOutputMessageWebSearchToolCall
       description: >-
         Web search tool call output message for OpenAI responses.
+    OpenAIResponsePrompt:
+      type: object
+      properties:
+        id:
+          type: string
+          description: Unique identifier of the prompt template
+        variables:
+          type: object
+          additionalProperties:
+            $ref: '#/components/schemas/OpenAIResponseInputMessageContent'
+          description: >-
+            Dictionary of variable names to OpenAIResponseInputMessageContent structure
+            for template substitution. The substitution values can either be strings,
+            or other Response input types like images or files.
+        version:
+          type: string
+          description: >-
+            Version number of the prompt to use (defaults to latest if not specified)
+      additionalProperties: false
+      required:
+        - id
+      title: OpenAIResponsePrompt
+      description: >-
+        OpenAI compatible Prompt object that is used in OpenAI responses.
     OpenAIResponseText:
       type: object
       properties:
@@ -7293,6 +7358,10 @@ components:
         model:
           type: string
           description: The underlying LLM used for completions.
+        prompt:
+          $ref: '#/components/schemas/OpenAIResponsePrompt'
+          description: >-
+            (Optional) Prompt object with ID, version, and variables.
         instructions:
           type: string
         previous_response_id:
@@ -7370,6 +7439,10 @@ components:
           type: string
           description: >-
             (Optional) ID of the previous response in a conversation
+        prompt:
+          $ref: '#/components/schemas/OpenAIResponsePrompt'
+          description: >-
+            (Optional) Reference to a prompt template and its variables.
         status:
           type: string
           description: >-