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.
Example files like openai.py shadow installed packages when Python adds the
script directory to sys.path. Prepend the parent folder name to each example
file (e.g. openai.py -> function-calling-openai.py). Also split
thinking-and-mcp/ into separate mcp/ and thinking/ directories.
