docs(llm-router): add user guide notebook and update DESIGN.md

Add comprehensive Jupyter notebook (13_llm_router.ipynb) covering
pretrained routing, custom tiers, cost optimization, tier management,
serialization, and async usage. Update DESIGN.md with async support,
pretrained config details, and corrected model pricing.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: bsbodden