docs: 📚 restructure README with quick start guide and improved navigation

Complete overhaul of the README to improve first-time user experience and discoverability of features.

- Reorganize content with prominent "Quick Start" section at the top
- Add clear "Connecting to the Proxy" guide with model format explanation
- Group features into collapsible sections for better readability
- Consolidate credential management documentation with TUI and CLI instructions
- Add comprehensive usage examples for Python, curl, and popular chat UIs
- Move advanced configuration into collapsible details sections
- Improve OAuth provider documentation with per-provider setup guides
- Add troubleshooting table with common issues and solutions
- Restructure technical documentation links into organized table
- Emphasize universal compatibility and zero-code-change deployment

Author: Mirrowel