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/function-calling/function-calling-grok.py

@@ -62,10 +62,10 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     logger.info(f"Starting bot")
 
     async with aiohttp.ClientSession() as session:
-        stt = DeepgramSTTService(api_key=os.getenv("DEEPGRAM_API_KEY"))
+        stt = DeepgramSTTService(api_key=os.environ["DEEPGRAM_API_KEY"])
 
         tts = XAIHttpTTSService(
-            api_key=os.getenv("XAI_API_KEY"),
+            api_key=os.environ["XAI_API_KEY"],
             aiohttp_session=session,
             settings=XAIHttpTTSService.Settings(
                 voice="eve",
@@ -73,7 +73,7 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
         )
 
         llm = GrokLLMService(
-            api_key=os.getenv("XAI_API_KEY"),
+            api_key=os.environ["XAI_API_KEY"],
             settings=GrokLLMService.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.",
             ),