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/persistent-context/persistent-context-openai-realtime.py

@@ -93,6 +93,7 @@ async def load_conversation(params: FunctionCallParams):
         try:
             with open(filename) as file:
                 params.context.set_messages(json.load(file))
+                assert isinstance(params.llm, OpenAIRealtimeLLMService)
                 await params.llm.reset_conversation()
                 # NOTE: we manually create a response here rather than relying
                 # on the function callback to trigger one since we've reset the
@@ -171,10 +172,10 @@ transport_params = {
 async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     logger.info(f"Starting bot")
 
-    stt = DeepgramSTTService(api_key=os.getenv("DEEPGRAM_API_KEY"))
+    stt = DeepgramSTTService(api_key=os.environ["DEEPGRAM_API_KEY"])
 
     llm = OpenAIRealtimeLLMService(
-        api_key=os.getenv("OPENAI_API_KEY"),
+        api_key=os.environ["OPENAI_API_KEY"],
         settings=OpenAIRealtimeLLMService.Settings(
             system_instruction="""Your knowledge cutoff is 2023-10. You are a helpful and friendly AI.