Add preliminary support for multiple card games

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.

server/migrations/models/1_20260916235833_update.py

@@ -0,0 +1,42 @@
+from tortoise import BaseDBAsyncClient
+
+RUN_IN_TRANSACTION = True
+
+
+async def upgrade(db: BaseDBAsyncClient) -> str:
+    return """
+        ALTER TABLE "match" ADD "game_type" VARCHAR(32) NOT NULL DEFAULT 'scopone_scientifico';
+        CREATE INDEX IF NOT EXISTS "idx_match_game_ty_7d519c" ON "match" ("game_type");"""
+
+
+async def downgrade(db: BaseDBAsyncClient) -> str:
+    return """
+        DROP INDEX IF EXISTS "idx_match_game_ty_7d519c";
+        ALTER TABLE "match" DROP COLUMN "game_type";"""
+
+
+MODELS_STATE = (
+    "eJztmW1P4zgQgP9KlE+ctIdoYGF1Op2UlqLtLW0RLXenXa0sN3FTi8TO2s51K47/frbTNI"
+    "3zQgsUAeoXaGY8jv2MX2Ymd3ZEfRTywz4U3sz+zbqzCYyQ/FFUfLBsGMe5WAkEnIRpy1WT"
+    "CRcMekIKpzDkSIp8xD2GY4EpUU1dy6NRHCKBfEubWXRqUYLUPzFDFkMB5gIxqQ7kOCyxiB"
+    "E/VH371JOdYxI8rZuE4B8JAoIGSDZksrNv36UYEx/9RDx7jG/BFKPQLwDBvupAy4HqUMlu"
+    "bnrnF7qlGuIEeDRMIpK3jhdiRsmqeZJg/1DZKF2ACGJQTmENF0nCcIk1E6UjlgLBErQaqp"
+    "8LfDSFSaig279PE+Ip1pZ+k/pz8sdyaGvNABgMx2DUHQNgl3ykhmDwXoo8SpR/MREK1N19"
+    "2m8OREtt9YLOZ/f64Pj0F42AchEwrdS47HttCAVMTTX0nLLyV8qrBLszg6wadsHIYC6H/B"
+    "jamaAJN/doLFcd4B5GROAp9uiuYMtN9hOEiARC7dJjpwH+X+51yt/R/Knckek+HSw1jlYp"
+    "N+TYBYIRgHImlFWQH0UwDHtEVNM3bQ0HyCk8jwPyMyWDm+HbBfBADeLXY+fs9JPU6jGqh7"
+    "MG8qO+e3nZG4yr2E6ewHayZ1vHdo6JnDpQmLY5MAyzXR0ZL0u1cES0NjghWrUHRKt0PkAm"
+    "b8xHrmHDdr+Gi2xnkPgcxCFcoIoQo5mtabtnW2TL5eKT8wZQlMmeSyICR6iabNHS4OovTQ"
+    "+zH2+QcgPMca/fHY3d/pXqPuL8R6h5ueOu0jhaujCkB6fGabLqxPq7N/5sqUfr63DQNYPC"
+    "VbvxV1uNCSaCAkLnAPrrTDJxJiq4eYoJ5rNH+dkw3Tv61TlaZWTT27VsQQkm0LudQ+aDgi"
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+    "vakCWV05ISf6QFEhvdjYZrWFK3leYw/H2qdZQSDhiFmY6N+6y3IxYQu7iurBt7z8oWwATy"
+    "b2931J4TWVFFZ+2SJBWLd5sYLCiyUHzsePG6QHslVtgqB1xVDLx1xtV6Cft0Bt2r3DZMw5"
+    "OtqE99FRPW+lM0JbVBXsNKcLmc0+TSiXaLZZs/vCQc06LRUO5ml8ZcRglIYIkpraTGVENp"
+    "Emb5BtA8z2cHhZCLvbvbGB9abf7ma0ZSMstLi8fNNgabtoYt3mOWOK1wv8gRCilGYYfMtw"
+    "LyhDOCBf0EIj7smBQOJVXWLmx7S3CbWUSUgxg/NVYFtYU3L2cs4oXbIdd9Rxz7v2fX3qts"
+    "ukxEUMV3/eXGo+NKUiMG/zUBJST/SZPzzW3vCVG7rifl+672nZwe4vd6d1cnby6fj0ZHXD"
+    "ryRN13x2RNYnBf8ixnHV3VR/6a+ZvMN7fyc5gdpUWxBeNn+HdFsbZQCthgygVc4A5BsFIh"
+    "VJwJ+j4aCa8JqJWenEnrD+s0LM32Iu0ABXwSjEWRnTg777j4m7czlsm/GB6qBdFSC85GV2"
+    "/z8H5XI/"
+)