docs: enhance gateway and SDK quickstart documentation

docs/my-website/docs/learn/gateway_quickstart.md

@@ -59,7 +59,7 @@ curl -X POST 'http://0.0.0.0:4000/chat/completions' \
 
 ## 6. Check The Response
 
-If the request succeeds, the proxy returns `200 OK` with the same OpenAI-style response shape LiteLLM uses in the SDK.
+If the request succeeds, the proxy returns `200 OK` with an OpenAI-style response.
 
 The assistant text will be in:
 
@@ -67,33 +67,48 @@ The assistant text will be in:
 choices[0].message.content
 ```
 
-It looks like this:
+If your gateway is routing to OpenAI, a real response can look like this:
 
 ```json
 {
   "id": "chatcmpl-abc123",
-  "object": "chat.completion",
   "created": 1677858242,
-  "model": "gpt-4o-mini",
+  "model": "gpt-4o-mini-2024-07-18",
+  "object": "chat.completion",
+  "system_fingerprint": "fp_406d6473f8",
   "choices": [
     {
+      "finish_reason": "stop",
       "index": 0,
       "message": {
         "role": "assistant",
-        "content": "Hello! How can I help?"
-      },
-      "finish_reason": "stop"
+        "content": "Hello! How can I assist you today?",
+        "tool_calls": null,
+        "function_call": null,
+        "annotations": []
+      }
     }
   ],
   "usage": {
-    "prompt_tokens": 12,
     "completion_tokens": 9,
-    "total_tokens": 21
-  }
+    "prompt_tokens": 13,
+    "total_tokens": 22,
+    "completion_tokens_details": {
+      "accepted_prediction_tokens": 0,
+      "audio_tokens": 0,
+      "reasoning_tokens": 0,
+      "rejected_prediction_tokens": 0
+    },
+    "prompt_tokens_details": {
+      "audio_tokens": 0,
+      "cached_tokens": 0
+    }
+  },
+  "service_tier": "default"
 }
 ```
 
-`id`, `created`, token counts, and message text will vary by request.
+`id`, `created`, the resolved model version, token counts, and message text will vary by request. Other providers may return a smaller or slightly different set of fields, but `choices[0].message.content` is the main field to read.
 
 ## 7. Add Keys And The UI
 

docs/my-website/docs/learn/sdk_quickstart.md

@@ -56,7 +56,48 @@ prints the assistant text, for example:
 Hello! I'm doing well, thanks for asking.
 ```
 
-The full response is an OpenAI-style `ModelResponse` object. It looks like this:
+If you print the full object with:
+
+```python
+print(response)
+```
+
+you will see a Python `ModelResponse(...)` object. For an OpenAI-backed model, it can look like this:
+
+```python
+ModelResponse(
+    id='chatcmpl-abc123',
+    created=1773782130,
+    model='gpt-4o-2024-08-06',
+    object='chat.completion',
+    system_fingerprint='fp_4ff89bf575',
+    choices=[
+        Choices(
+            finish_reason='stop',
+            index=0,
+            message=Message(
+                content="Hello! I'm just a program, but I'm here to help you. How can I assist you today?",
+                role='assistant',
+                tool_calls=None,
+                function_call=None,
+                provider_specific_fields={'refusal': None},
+                annotations=[]
+            ),
+            provider_specific_fields={}
+        )
+    ],
+    usage=Usage(
+        completion_tokens=21,
+        prompt_tokens=13,
+        total_tokens=34,
+        completion_tokens_details=CompletionTokensDetailsWrapper(...),
+        prompt_tokens_details=PromptTokensDetailsWrapper(...)
+    ),
+    service_tier='default'
+)
+```
+
+The same response follows an OpenAI-style shape. Conceptually, it looks like this:
 
 ```json
 {
@@ -82,7 +123,9 @@ The full response is an OpenAI-style `ModelResponse` object. It looks like this:
 }
 ```
 
-`id`, `created`, token counts, and message text will vary by request. For the full output reference, see [completion output](/docs/completion/output).
+`id`, `created`, token counts, and message text will vary by request.
+
+If you call an OpenAI-backed model, you may also see extra fields such as `system_fingerprint`, `service_tier`, `tool_calls`, `function_call`, `annotations`, `provider_specific_fields`, and detailed token usage. For the full output reference, see [completion output](/docs/completion/output).
 
 Need more provider examples? See the main [Getting Started](/docs/#quick-start) page.