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-openai-async.py

@@ -70,7 +70,7 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     logger.info(f"Starting bot")
 
     stt = OpenAISTTService(
-        api_key=os.getenv("OPENAI_API_KEY"),
+        api_key=os.environ["OPENAI_API_KEY"],
         settings=OpenAISTTService.Settings(
             model="gpt-4o-transcribe",
             prompt="Expect words related weather, such as temperature and conditions. And restaurant names.",
@@ -78,7 +78,7 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     )
 
     tts = OpenAITTSService(
-        api_key=os.getenv("OPENAI_API_KEY"),
+        api_key=os.environ["OPENAI_API_KEY"],
         settings=OpenAITTSService.Settings(
             voice="ballad",
         ),
@@ -86,7 +86,7 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     )
 
     llm = OpenAILLMService(
-        api_key=os.getenv("OPENAI_API_KEY"),
+        api_key=os.environ["OPENAI_API_KEY"],
         enable_async_tool_cancellation=True,
         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.",