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-gemini-live-vertex-function-calling.py

@@ -110,8 +110,8 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
 
     llm = GeminiLiveVertexLLMService(
         credentials=os.getenv("GOOGLE_VERTEX_TEST_CREDENTIALS"),
-        project_id=os.getenv("GOOGLE_CLOUD_PROJECT_ID"),
-        location=os.getenv("GOOGLE_CLOUD_LOCATION"),
+        project_id=os.environ["GOOGLE_CLOUD_PROJECT_ID"],
+        location=os.environ["GOOGLE_CLOUD_LOCATION"],
         settings=GeminiLiveVertexLLMService.Settings(
             system_instruction=system_instruction,
             voice="Puck",  # Aoede, Charon, Fenrir, Kore, Puck