docs(response_api): move file_search details to dedicated tutorial

Replace inline file_search documentation in response_api.md with a canonical link and add the new tutorial to sidebars so users discover the usage-first guide.

Made-with: Cursor

docs/my-website/docs/response_api.md

@@ -1558,132 +1558,9 @@ curl -X POST "http://localhost:4000/v1/responses" \
 
 ## File Search (Vector Stores)
 
-The **file_search** tool lets the model search your vector stores and cite retrieved content in its answer (OpenAI Responses API format). Pass `tools=[{"type": "file_search", "vector_store_ids": [...]}]`. The response includes a `file_search_call` output item and `file_citation` annotations on the answer text.
+For full `file_search` usage (native + emulated fallback), SDK/Proxy examples, architecture diagram, and Q&A, see:
 
-**Supported providers:** `openai`, `azure` (native). Other providers will receive an `UnsupportedParamsError` until the emulated-fallback path is available.
-
-:::note
-If you are using LiteLLM-managed vector stores (created via `/v1/vector_stores`), pass the LiteLLM vector store ID directly — LiteLLM automatically decodes it to the provider-native ID before sending the request.
-:::
-
-### Python SDK
-
-```python showLineNumbers title="File search with LiteLLM Python SDK"
-import litellm
-
-response = litellm.responses(
-    model="openai/gpt-4.1",
-    input="What is deep research?",
-    tools=[{
-        "type": "file_search",
-        "vector_store_ids": ["vs_abc123"]  # native or LiteLLM-managed vector store ID
-    }],
-)
-
-# Output contains a file_search_call item followed by the answer with citations
-for item in response.output:
-    if item.type == "file_search_call":
-        print("Queries:", item.queries)
-    elif item.type == "message":
-        for block in item.content:
-            print(block.text)
-            for ann in block.annotations:
-                print(f"  ↳ {ann.filename} (file_id={ann.file_id})")
-```
-
-#### Response Format
-
-```json
-{
-  "output": [
-    {
-      "type": "file_search_call",
-      "id": "fs_67c09ccea8c48191ade9367e3ba71515",
-      "status": "completed",
-      "queries": ["What is deep research?"],
-      "search_results": null
-    },
-    {
-      "id": "msg_67c09cd3091c819185af2be5d13d87de",
-      "type": "message",
-      "role": "assistant",
-      "content": [
-        {
-          "type": "output_text",
-          "text": "Deep research is a capability that allows for extensive inquiry ...",
-          "annotations": [
-            {
-              "type": "file_citation",
-              "index": 992,
-              "file_id": "file-2dtbBZdjtDKS8eqWxqbgDi",
-              "filename": "deep_research_blog.pdf"
-            }
-          ]
-        }
-      ]
-    }
-  ]
-}
-```
-
-### LiteLLM Proxy (AI Gateway)
-
-**OpenAI Python SDK (proxy as base_url):**
-
-```python showLineNumbers title="File search via LiteLLM Proxy"
-from openai import OpenAI
-
-client = OpenAI(
-    base_url="http://localhost:4000",
-    api_key="your-proxy-api-key",
-)
-
-response = client.responses.create(
-    model="openai/gpt-4.1",
-    input="Summarise the Q3 earnings report.",
-    tools=[{
-        "type": "file_search",
-        "vector_store_ids": ["vs_abc123"]
-    }],
-)
-```
-
-**curl:**
-
-```bash title="File search via curl to LiteLLM Proxy"
-curl -X POST "http://localhost:4000/v1/responses" \
-  -H "Content-Type: application/json" \
-  -H "Authorization: Bearer your-proxy-api-key" \
-  -d '{
-    "model": "openai/gpt-4.1",
-    "input": "Summarise the Q3 earnings report.",
-    "tools": [{"type": "file_search", "vector_store_ids": ["vs_abc123"]}]
-  }'
-```
-
-### Using LiteLLM-Managed Vector Stores
-
-If you created a vector store through LiteLLM (`POST /v1/vector_stores/new`), use the returned `vector_store_id` directly. LiteLLM decodes the unified ID to the provider-native vector store ID automatically.
-
-```python showLineNumbers title="File search with LiteLLM-managed vector store"
-from openai import OpenAI
-
-client = OpenAI(base_url="http://localhost:4000", api_key="your-proxy-api-key")
-
-# vector_store_id returned by POST /v1/vector_stores/new
-managed_vs_id = "bGl0ZWxsbV9wcm94eTo..."   # LiteLLM-managed ID
-
-response = client.responses.create(
-    model="openai/gpt-4.1",
-    input="What does the documentation say about authentication?",
-    tools=[{"type": "file_search", "vector_store_ids": [managed_vs_id]}],
-)
-```
-
-LiteLLM will:
-1. Verify the calling team has access to the vector store.
-2. Decode the managed ID to the provider-native vector store ID.
-3. Forward the request to the provider unchanged.
+- [`File Search in the Responses API — E2E Testing Guide`](/docs/tutorials/file_search_responses_api)
 
 ## Session Management
 

docs/my-website/sidebars.js

@@ -1054,6 +1054,7 @@ const sidebars = {
           label: "AI Coding Tools (OpenWebUI, Claude Code, Gemini CLI, OpenAI Codex, etc.)",
           href: "/docs/ai_tools",
         },
+        "tutorials/file_search_responses_api",
         "tutorials/anthropic_file_usage",
         "tutorials/default_team_self_serve",
         "tutorials/msft_sso",