Fixes for multi-turn tool calls in Responses API

Testing with Codex locally, I found another issue in how we were
plumbing through tool calls in multi-turn scenarios and the way tool
call inputs and outputs from previous turns were passed back into
future turns.

This led me to realize we were missing the function tool call output
type in the Responses API, so this adds that and plumbs handling of it
through the responses API to chat completion conversion code.

Signed-off-by: Ben Browning <bbrownin@redhat.com>

docs/_static/llama-stack-spec.yaml

@@ -4537,7 +4537,34 @@ components:
     OpenAIResponseInput:
       oneOf:
         - $ref: '#/components/schemas/OpenAIResponseOutputMessageWebSearchToolCall'
+        - $ref: '#/components/schemas/OpenAIResponseOutputMessageFunctionToolCall'
+        - $ref: '#/components/schemas/OpenAIResponseInputFunctionToolCallOutput'
         - $ref: '#/components/schemas/OpenAIResponseMessage'
+    "OpenAIResponseInputFunctionToolCallOutput":
+      type: object
+      properties:
+        call_id:
+          type: string
+        output:
+          type: string
+        type:
+          type: string
+          const: function_call_output
+          default: function_call_output
+        id:
+          type: string
+        status:
+          type: string
+      additionalProperties: false
+      required:
+        - call_id
+        - output
+        - type
+      title: >-
+        OpenAIResponseInputFunctionToolCallOutput
+      description: >-
+        This represents the output of a function call that gets passed back to the
+        model.
     OpenAIResponseInputMessageContent:
       oneOf:
         - $ref: '#/components/schemas/OpenAIResponseInputMessageContentText'
@@ -4721,6 +4748,33 @@ components:
         - type
       title: >-
         OpenAIResponseOutputMessageContentOutputText
+    "OpenAIResponseOutputMessageFunctionToolCall":
+      type: object
+      properties:
+        arguments:
+          type: string
+        call_id:
+          type: string
+        name:
+          type: string
+        type:
+          type: string
+          const: function_call
+          default: function_call
+        id:
+          type: string
+        status:
+          type: string
+      additionalProperties: false
+      required:
+        - arguments
+        - call_id
+        - name
+        - type
+        - id
+        - status
+      title: >-
+        OpenAIResponseOutputMessageFunctionToolCall
     "OpenAIResponseOutputMessageWebSearchToolCall":
       type: object
       properties:
@@ -4840,33 +4894,6 @@ components:
           message: '#/components/schemas/OpenAIResponseMessage'
           web_search_call: '#/components/schemas/OpenAIResponseOutputMessageWebSearchToolCall'
           function_call: '#/components/schemas/OpenAIResponseOutputMessageFunctionToolCall'
-    "OpenAIResponseOutputMessageFunctionToolCall":
-      type: object
-      properties:
-        arguments:
-          type: string
-        call_id:
-          type: string
-        name:
-          type: string
-        type:
-          type: string
-          const: function_call
-          default: function_call
-        id:
-          type: string
-        status:
-          type: string
-      additionalProperties: false
-      required:
-        - arguments
-        - call_id
-        - name
-        - type
-        - id
-        - status
-      title: >-
-        OpenAIResponseOutputMessageFunctionToolCall
     OpenAIResponseObjectStream:
       oneOf:
         - $ref: '#/components/schemas/OpenAIResponseObjectStreamResponseCreated'