feat(responses)!: Add web_search_2025_08_26 to the WebSearchToolTypes (#4103)

# What does this PR do?
Resolves #4102 

1. Added `web_search_2025_08_26` to the `WebSearchToolTypes` list and
the `OpenAIResponseInputToolWebSearch.type` Literal union
2. No changes needed to tool execution logic - all `web_search` types
map to the same underlying tool
3. Backward compatibility is maintained - existing `web_search`,
`web_search_preview`, and `web_search_preview_2025_03_11` types continue
to work
4. Added an integration test case using {"type":
"web_search_2025_08_26"} to verify it works correctly
5. Updated `docs/docs/providers/openai_responses_limitations.mdx` to
reflect that `web_search_2025_08_26` is now supported.
6. Removed incorrect references to `MOD1/MOD2/MOD3` (which don't exist
in the codebase)


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## Test Plan
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---------

Signed-off-by: Aakanksha Duggal <aduggal@redhat.com>
Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>

docs/docs/providers/openai_responses_limitations.mdx

@@ -48,11 +48,9 @@ Both OpenAI and Llama Stack support a web-search built-in tool.  The [OpenAI doc
 
 > The type of the web search tool. One of `web_search` or `web_search_2025_08_26`.
 
-In contrast, the [Llama Stack documentation](https://llamastack.github.io/docs/api/create-a-new-open-ai-response) says that the allowed values for `type` for web search are `MOD1`, `MOD2` and `MOD3`.
-Is that correct?  If so, what are the meanings of each of them?  It might make sense for the allowed values for OpenAI map to some values for Llama Stack so that code written to the OpenAI specification
-also work with Llama Stack.
+Llama Stack now supports both `web_search` and `web_search_2025_08_26` types, matching OpenAI's API. For backward compatibility, Llama Stack also supports `web_search_preview` and `web_search_preview_2025_03_11` types.
 
-The OpenAI web search tool also has fields for `filters` and `user_location` which are not documented as options for Llama Stack.  If feasible, it would be good to support these too.
+The OpenAI web search tool also has fields for `filters` and `user_location` which are not yet implemented in Llama Stack.  If feasible, it would be good to support these too.
 
 ---
 

docs/static/llama-stack-spec.yaml

@@ -6075,6 +6075,8 @@ components:
               const: web_search_preview
             - type: string
               const: web_search_preview_2025_03_11
+            - type: string
+              const: web_search_2025_08_26
           default: web_search
           description: Web search tool type variant to use
         search_context_size:

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

@@ -6791,6 +6791,8 @@ components:
               const: web_search_preview
             - type: string
               const: web_search_preview_2025_03_11
+            - type: string
+              const: web_search_2025_08_26
           default: web_search
           description: Web search tool type variant to use
         search_context_size: