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>

client-sdks/stainless/openapi.yml

@@ -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: