A game-type registry (server/src/tavolo/games.py) is now the single
source of truth for the games the platform can host; only scopone
scientifico is registered so far. GET /api/game-types exposes it for the
lobby's new game dropdown, and POST /api/games accepts a validated
game_type (default scopone_scientifico) which is carried on the live
GameState and onto each finished Match row (new indexed column,
migration 1_20260916235833_update), so statistics can be scoped per
game: /api/me/matches and /api/leaderboard take an optional game_type
filter and every serialized match includes its game_type.
Game states serialized before this change still load with the default
game type.
