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/tts/tts-deepgram-sagemaker.py

@@ -50,16 +50,16 @@ 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 = DeepgramSageMakerTTSService(
-        endpoint_name=os.getenv("SAGEMAKER_TTS_ENDPOINT_NAME"),
-        region=os.getenv("AWS_REGION"),
+        endpoint_name=os.environ["SAGEMAKER_TTS_ENDPOINT_NAME"],
+        region=os.environ["AWS_REGION"],
         voice="aura-2-helena-en",
     )
 
     llm = OpenAILLMService(
-        api_key=os.getenv("OPENAI_API_KEY"),
+        api_key=os.environ["OPENAI_API_KEY"],
         settings=OpenAILLMService.Settings(
             system_instruction="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.",
         ),