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/video-avatar/video-avatar-tavus-transport.py

@@ -37,8 +37,8 @@ async def main():
     async with aiohttp.ClientSession() as session:
         transport = TavusTransport(
             bot_name="Pipecat bot",
-            api_key=os.getenv("TAVUS_API_KEY"),
-            replica_id=os.getenv("TAVUS_REPLICA_ID"),
+            api_key=os.environ["TAVUS_API_KEY"],
+            replica_id=os.environ["TAVUS_REPLICA_ID"],
             session=session,
             params=TavusParams(
                 audio_in_enabled=True,
@@ -47,17 +47,17 @@ async def main():
             ),
         )
 
-        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="a167e0f3-df7e-4d52-a9c3-f949145efdab",
             ),
         )
 
         llm = GoogleLLMService(
-            api_key=os.getenv("GOOGLE_API_KEY"),
+            api_key=os.environ["GOOGLE_API_KEY"],
             settings=GoogleLLMService.Settings(
                 system_instruction="You are a helpful assistant in a voice conversation. Your responses will be spoken aloud, so avoid emojis, bullet points, or other formatting that can't be spoken. Respond to what the user said in a creative, helpful, and brief way.",
             ),