Badges page and Leaderboard page exist on frontend but backend has no real gamification engine. No XP tracking, no streak system, no achievement conditions engine. Badges appear hardcoded on frontend.

Implement: XP system (actions → XP → levels), streaks (consecutive study days), achievements engine (condition definitions in DB), leaderboard by XP.

Closes gap against: Coursemology (full gamification), Duolingo (streaks + XP), Brilliant (streak engagement)

Effort: L