E2E: Playwright (register → login → create match → play → view stats)

[BolanosDavid]

Goal

Ensure the system covers the main user flow end-to-end.

Tasks

• Set up Playwright (if not already configured).
• Test: register/login.
• Test: create match + play 2–3 turns (mock if needed) + persist.
• Test: stats page shows updated results.

Acceptance Criteria

• Tests pass in CI (or at least locally) consistently.

Dependencies

• Issue 49 (Webapp: Implement real login/register + session management (JWT) #49)
• Issue 51 (Game API: POST /api/game/matches (create match with size/strategy/difficulty) #51)
• Issue 53 (Game API: POST /api/game/matches/:id/moves (atomic persistence) #53)
• Issue 57 (Gamey API: POST /api/gamey/play (YEN in → next_move YEN out) #57)
• Issue 62 (Webapp Stats: Display user statistics and match history #62)