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-sarvam.py

@@ -64,21 +64,21 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     logger.info(f"Starting bot")
 
     stt = SarvamSTTService(
-        api_key=os.getenv("SARVAM_API_KEY"),
+        api_key=os.environ["SARVAM_API_KEY"],
         settings=SarvamSTTService.Settings(
             model="saaras:v3",
         ),
     )
 
     tts = SarvamTTSService(
-        api_key=os.getenv("SARVAM_API_KEY"),
+        api_key=os.environ["SARVAM_API_KEY"],
         settings=SarvamTTSService.Settings(
             model="bulbul:v3",
             voice="shubh",
         ),
     )
     llm = SarvamLLMService(
-        api_key=os.getenv("SARVAM_API_KEY"),
+        api_key=os.environ["SARVAM_API_KEY"],
         settings=SarvamLLMService.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.",
         ),