docs: FULL_SYNC_PLAN — complete management↔player integration roadmap

Comprehensive plan documenting:
- 11 features player app writes that management can't see
- 10 management features player app doesn't integrate with
- 7 upgrade phases with estimated ~20 hours total effort
- Database functions needed (atomic coin award, ban check)
- 7 new management modules needed (rewards-config, seasons, etc.)
- Architecture diagram showing both systems' data flow
- Security gaps (no rate limit, no ban enforcement, no validation)
- Priority-ordered execution plan

Based on parallel audits of:
- el3ab-management: 38 modules, 425+ routes, tournament/player/economy systems
- el3ab-player: 27 API endpoints, tables used, admin visibility needs

Key finding: Both systems work independently but critical bridges are missing
(tournament registration, match visibility, reward configuration, ban enforcement)
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>