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/tests/test_stats.py

@@ -66,11 +66,13 @@ class SaveMatchResultTest(unittest.TestCase):
             assert match is not None
             self.assertEqual(state.scores[0], match.team_a_score)
             self.assertEqual("A", match.winner_team)
+            # The game type travels from the live state onto the row.
+            self.assertEqual("scopone_scientifico", match.game_type)
             winners = await MatchPlayer.filter(won=True)
             self.assertEqual({"alice", "carol"}, {p.user_sub for p in winners})
 
 
-async def _seed_two_matches() -> None:
+async def _seed_two_matches(game_types: tuple = ("scopone_scientifico", "scopone_scientifico")) -> None:
     ctx = await _use_app_db()
     with ctx:
         for index, (a_score, b_score, winner, finished) in enumerate(
@@ -81,6 +83,7 @@ async def _seed_two_matches() -> None:
         ):
             match = await Match.create(
                 id=uuid.uuid4(),
+                game_type=game_types[index],
                 team_a_score=a_score,
                 team_b_score=b_score,
                 winner_team=winner,
@@ -165,5 +168,45 @@ class StatsRouteTest(unittest.TestCase):
         self.assertEqual("alice", response.json()["results"][0]["user_sub"])
 
 
+class GameTypeFilterTest(unittest.TestCase):
+    """Stats endpoints scope results by the match's game type."""
+
+    @async_test
+    async def test_my_matches_filter_by_game_type(self) -> None:
+        # The second seed names a game the registry does not know; rows are
+        # written directly, so this only exercises the SQL filter.
+        await _seed_two_matches(game_types=("scopone_scientifico", "other_game"))
+        transport = ASGITransport(app=app)
+        async with AsyncClient(transport=transport, base_url="http://127.0.0.1") as client:
+            with oidc_user("alice"):
+                all_matches = await client.get("/api/me/matches")
+                scoped = await client.get("/api/me/matches?game_type=scopone_scientifico")
+                unknown = await client.get("/api/me/matches?game_type=briscola")
+            self.assertEqual(2, len(all_matches.json()["results"]))
+            self.assertEqual(
+                {"scopone_scientifico", "other_game"},
+                {m["game_type"] for m in all_matches.json()["results"]},
+            )
+            scoped_results = scoped.json()["results"]
+            self.assertEqual(1, len(scoped_results))
+            self.assertEqual("scopone_scientifico", scoped_results[0]["game_type"])
+            self.assertEqual(400, unknown.status_code)
+
+    @async_test
+    async def test_leaderboard_filter_by_game_type(self) -> None:
+        await _seed_two_matches(game_types=("scopone_scientifico", "other_game"))
+        transport = ASGITransport(app=app)
+        async with AsyncClient(transport=transport, base_url="http://127.0.0.1") as client:
+            scoped = await client.get("/api/leaderboard?game_type=scopone_scientifico")
+            unknown = await client.get("/api/leaderboard?game_type=briscola")
+        self.assertEqual(200, scoped.status_code)
+        by_sub = {row["user_sub"]: row for row in scoped.json()["results"]}
+        # Only the first match counts: one match per player, team A won.
+        self.assertEqual(1, by_sub["alice"]["matches"])
+        self.assertEqual(1, by_sub["alice"]["wins"])
+        self.assertEqual(0, by_sub["bob"]["wins"])
+        self.assertEqual(400, unknown.status_code)
+
+
 if __name__ == "__main__":
     unittest.main()