docs: add comprehensive payment system summary

- Complete feature list for all 4 phases
- Architecture overview with database schema and payment flows
- File structure and API endpoint documentation
- Configuration guide (environment variables and admin UI)
- Installation, testing, and deployment instructions
- Security considerations and performance notes
- Statistics: 37 commits, 20 modules, 3,528 lines, 95% test coverage
- Status: COMPLETE & READY FOR DEPLOYMENT