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/update-settings/llm/llm-azure-realtime.py

@@ -10,6 +10,7 @@ import os
 from dotenv import load_dotenv
 from loguru import logger
 
+from pipecat.adapters.base_llm_adapter import LLMContextMessage
 from pipecat.audio.vad.silero import SileroVADAnalyzer
 from pipecat.frames.frames import LLMRunFrame, LLMUpdateSettingsFrame
 from pipecat.pipeline.pipeline import Pipeline
@@ -51,11 +52,11 @@ async def run_bot(transport: BaseTransport, runner_args: RunnerArguments):
     logger.info(f"Starting bot")
 
     llm = AzureRealtimeLLMService(
-        api_key=os.getenv("AZURE_REALTIME_API_KEY"),
-        base_url=os.getenv("AZURE_REALTIME_BASE_URL"),
+        api_key=os.environ["AZURE_REALTIME_API_KEY"],
+        base_url=os.environ["AZURE_REALTIME_BASE_URL"],
     )
 
-    messages = [
+    messages: list[LLMContextMessage] = [
         {
             "role": "system",
             "content": "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.",