Implement Analytics Module for Player and Puzzle Insights

[Mkalbani]

Description

Create an analytics module that aggregates and exposes data insights for both players and puzzle performance. Understanding how players interact with puzzles helps the game improve over time — which puzzles have high abandon rates, which are solved fastest, where players drop off. This module feeds dashboards and informs content decisions.

Acceptance Criteria

• An analytics module is scaffolded at src/analytics/
• GET /analytics/puzzles/:id returns solve rate, average time, average score, and hint usage rate
• GET /analytics/player/:userId returns sessions played, puzzles solved, and average score
• GET /analytics/overview (admin-only) returns platform-wide aggregates
• Analytics are computed from raw session and score data — not manually maintained
• Responses are cached for a configurable TTL to reduce DB load
• Date range filtering is supported via from and to query params
• Unit tests cover each analytics endpoint and cache behaviour