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.

web/src/model.rs

@@ -101,6 +101,9 @@ pub struct GameView {
     pub id: String,
     #[serde(default)]
     pub join_code: String,
+    /// Which card game this match is (id from /api/game-types).
+    #[serde(default)]
+    pub game_type: String,
     pub phase: String,
     #[serde(default)]
     pub target_score: i32,
@@ -174,6 +177,8 @@ pub struct MatchPlayer {
 #[allow(dead_code)]
 pub struct MatchSummary {
     pub id: String,
+    #[serde(default)]
+    pub game_type: String,
     pub team_a_score: i32,
     pub team_b_score: i32,
     pub winner_team: String,
@@ -211,6 +216,22 @@ pub struct LeaderboardPage {
     pub results: Vec<LeaderboardEntry>,
 }
 
+/// A card game the platform can host (GET /api/game-types).
+#[derive(Debug, Clone, PartialEq, Deserialize)]
+#[allow(dead_code)]
+pub struct GameTypeInfo {
+    pub id: String,
+    pub name: String,
+    #[serde(default)]
+    pub description: String,
+}
+
+#[derive(Debug, Clone, Deserialize)]
+pub struct GameTypesPage {
+    #[serde(default)]
+    pub results: Vec<GameTypeInfo>,
+}
+
 /// Map a card code (e.g. `07D`) to its asset path.
 pub fn card_asset(code: &str) -> String {
     format!("/assets/cards/{code}.svg")