Include examples in type checking

Remove `examples/` from the `pyrightconfig.json` ignore list and fix
the resulting type errors across all example files. Common fixes:

- Required API keys: `os.getenv("X")` -> `os.environ["X"]` so the
  return type is `str` rather than `str | None`, and misconfiguration
  fails fast.
- Narrow `LLMContextMessage` union members with `isinstance(..., dict)`
  before dict-style access.
- `assert isinstance(params.llm, ...)` before calling service-specific
  methods that aren't on the base `LLMService`.
- Guard optional frame fields (e.g. `LLMSearchResponseFrame.search_result`)
  before use.

examples/update-settings/llm/llm-perplexity.py

@@ -50,25 +50,18 @@ transport_params = {
 async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     logger.info(f"Starting bot")
 
-    stt = DeepgramSTTService(api_key=os.getenv("DEEPGRAM_API_KEY"))
+    stt = DeepgramSTTService(api_key=os.environ["DEEPGRAM_API_KEY"])
 
     tts = CartesiaTTSService(
-        api_key=os.getenv("CARTESIA_API_KEY"),
+        api_key=os.environ["CARTESIA_API_KEY"],
         settings=CartesiaTTSService.Settings(
             voice="71a7ad14-091c-4e8e-a314-022ece01c121",  # British Reading Lady
         ),
     )
 
-    llm = PerplexityLLMService(api_key=os.getenv("PERPLEXITY_API_KEY"))
+    llm = PerplexityLLMService(api_key=os.environ["PERPLEXITY_API_KEY"])
 
-    messages = [
-        {
-            "role": "developer",
-            "content": "You are a helpful assistant in a voice conversation. Your responses will be spoken aloud, so avoid emojis, bullet points, or other formatting that can't be spoken. Respond to what the user said in a creative, helpful, and brief way. Start by introducing yourself.",
-        },
-    ]
-
-    context = LLMContext(messages)
+    context = LLMContext()
     user_aggregator, assistant_aggregator = LLMContextAggregatorPair(
         context,
         user_params=LLMUserAggregatorParams(vad_analyzer=SileroVADAnalyzer()),
@@ -98,6 +91,9 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     @transport.event_handler("on_client_connected")
     async def on_client_connected(transport, client):
         logger.info(f"Client connected")
+        context.add_message(
+            {"role": "developer", "content": "Please introduce yourself to the user."}
+        )
         await task.queue_frames([LLMRunFrame()])
 
         await asyncio.sleep(10)