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/realtime/realtime-inworld.py

@@ -84,7 +84,7 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     # llm_model can be any supported model or an Inworld Router.
     # See: https://docs.inworld.ai/router/introduction
     llm = InworldRealtimeLLMService(
-        api_key=os.getenv("INWORLD_API_KEY"),
+        api_key=os.environ["INWORLD_API_KEY"],
         llm_model="xai/grok-4-1-fast-non-reasoning",
         voice="Sarah",
         settings=InworldRealtimeLLMService.Settings(