docs: update persistence examples for new declarative API

- Update example 09 (localStorage) to use field-based persistence
- Update example 10 (Supabase) to use field-based persistence
- Add documentation for advanced configuration options
- Add documentation for multiple adapters
- Add documentation for custom fields
- Add troubleshooting section for real-time sync
- Simplify example code by removing manual persistence logic

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Co-Authored-By: Claude <[email protected]>

Author: Max Carlson