Rewrite chess-api in TypeScript with clean game API + timed clocks

[rudi-rudi-rudi]

Summary

This PR fully replaces the legacy API with a clean TypeScript implementation focused on a general-purpose chess game API.

What changed

• Removed legacy v1 code paths and old Mongo/highscore architecture
• Introduced a clean game-centric API:
  • POST /v2/games
  • GET /v2/games/:id
  • DELETE /v2/games/:id
  • GET /v2/games/:id/moves?from=e2
  • POST /v2/games/:id/moves
  • POST /v2/games/:id/ai-move
  • POST /v2/games/:id/resign
• Added support for:
  • player-vs-player
  • player-vs-engine (simple built-in move chooser)
  • timed games with clocks + increment + timeout handling
• Modernized stack:
  • Fastify
  • chess.js (latest line)
  • TypeScript

Notes

• This is a foundational rewrite; persistence/auth/OpenAPI/tests can be layered in follow-up PRs.
• Current in-memory store is intentional for clean API reset and easier iteration.

[lilBunnyRabbit]

I don't like where this project is heading with all the "AI" changes...