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/stt/stt-assemblyai.py

@@ -51,21 +51,21 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     logger.info(f"Starting bot")
 
     stt = AssemblyAISTTService(
-        api_key=os.getenv("ASSEMBLYAI_API_KEY"),
+        api_key=os.environ["ASSEMBLYAI_API_KEY"],
         settings=AssemblyAISTTService.Settings(
             model="u3-rt-pro",
         ),
     )
 
     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 = 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. Try saying difficult names like 'Xiomara', 'Saoirse', or 'Krzystof' to test transcription accuracy.",
         ),