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-ultravox.py

@@ -166,7 +166,7 @@ There is also a secret menu that changes daily. If the user asks about it, use t
 
     llm = UltravoxRealtimeLLMService(
         params=OneShotInputParams(
-            api_key=os.getenv("ULTRAVOX_API_KEY"),
+            api_key=os.environ["ULTRAVOX_API_KEY"],
             system_prompt=system_prompt,
             temperature=0.3,
             max_duration=datetime.timedelta(minutes=3),