docs: Update README to reflect v0.3.0 project state

- Add Docker section with profile-based service management
- Add Installation Extras table (20+ optional extras)
- Add Makefile branch workflow (new-feat/pr/sync/done)
- Update CLI section with Interactive TUI + admin commands
- Add Playground section (FastAPI 17 routers + Next.js 15)
- Add Contributing section with Issue/PR templates
- Update Architecture section with project structure tree
- Mention beantui standalone TUI engine and MCP server
- Remove outdated Poetry installation instructions

Co-authored-by: Cursor <cursoragent@cursor.com>

Author: leebeanbin