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-user-email-gathering.py

@@ -60,13 +60,13 @@ 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"])
 
     # Cartesia offers a `<spell></spell>` tags that we can use to ask the user
     # to confirm the emails.
     # (see https://docs.cartesia.ai/build-with-sonic/formatting-text-for-sonic/spelling-out-input-text)
     tts = CartesiaTTSService(
-        api_key=os.getenv("CARTESIA_API_KEY"),
+        api_key=os.environ["CARTESIA_API_KEY"],
         settings=CartesiaTTSService.Settings(
             voice="71a7ad14-091c-4e8e-a314-022ece01c121",  # British Reading Lady
         ),
@@ -84,7 +84,7 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     # )
 
     llm = OpenAILLMService(
-        api_key=os.getenv("OPENAI_API_KEY"),
+        api_key=os.environ["OPENAI_API_KEY"],
         settings=OpenAILLMService.Settings(
             system_instruction="You need to gather a valid email or emails from the user. Your output will be spoken aloud, so avoid special characters that can't easily be spoken, such as emojis or bullet points. If the user provides one or more email addresses confirm them with the user. Enclose all emails with <spell> tags, for example <spell>a@a.com</spell>.",
         ),