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/features/features-live-translation.py

@@ -55,17 +55,17 @@ 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"])
 
     tts = CartesiaTTSService(
-        api_key=os.getenv("CARTESIA_API_KEY"),
+        api_key=os.environ["CARTESIA_API_KEY"],
         settings=CartesiaTTSService.Settings(
             voice="d4db5fb9-f44b-4bd1-85fa-192e0f0d75f9",  # Spanish-speaking Lady
         ),
     )
 
     llm = OpenAILLMService(
-        api_key=os.getenv("OPENAI_API_KEY"),
+        api_key=os.environ["OPENAI_API_KEY"],
         settings=OpenAILLMService.Settings(
             system_instruction="You are a live translation assistant. Your sole purpose is to translate English text into Spanish. When you receive English text from the user, immediately translate it into natural, fluent Spanish. Do not add explanations, commentary, or extra information—only provide the Spanish translation of the text you receive.",
         ),