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/pages/lobby.rs

@@ -4,7 +4,16 @@ use sycamore::prelude::*;
 use sycamore_router::navigate;
 
 use crate::api;
-use crate::model::User;
+use crate::model::{GameTypeInfo, User};
+
+/// Used when the game-types fetch fails: match creation must still work.
+fn fallback_game_types() -> Vec<GameTypeInfo> {
+    vec![GameTypeInfo {
+        id: "scopone_scientifico".to_string(),
+        name: "Scopone scientifico".to_string(),
+        description: String::new(),
+    }]
+}
 
 #[component]
 pub fn LobbyPage() -> View {
@@ -12,6 +21,8 @@ pub fn LobbyPage() -> View {
     let user = create_signal(Option::<Option<User>>::None);
     let error = create_signal(Option::<String>::None);
     let code = create_signal(String::new());
+    let game_types = create_signal(fallback_game_types());
+    let selected_game = create_signal("scopone_scientifico".to_string());
 
     spawn_local(async move {
         match api::me().await {
@@ -23,9 +34,20 @@ pub fn LobbyPage() -> View {
         }
     });
 
+    spawn_local(async move {
+        match api::game_types().await {
+            Ok(types) if !types.is_empty() => {
+                selected_game.set(types[0].id.clone());
+                game_types.set(types);
+            }
+            _ => {} // keep the scopone fallback
+        }
+    });
+
     let on_create = move |target: i32| {
+        let game_type = selected_game.get_clone();
         spawn_local(async move {
-            match api::create_game(target).await {
+            match api::create_game(&game_type, target).await {
                 Ok(game) => navigate(&format!("/game/{}", game.id)),
                 Err(e) => error.set(Some(e)),
             }
@@ -70,6 +92,14 @@ pub fn LobbyPage() -> View {
                         }
                         div(class="panel") {
                             h2 { "New match" }
+                            label(r#for="game-type") { "Game" }
+                            select(id="game-type", bind:value=selected_game) {
+                                Keyed(
+                                    list=game_types,
+                                    view=|g| view! { option(value=g.id.clone()) { (g.name) } },
+                                    key=|g| g.id.clone(),
+                                )
+                            }
                             p { "First team to reach the target score wins." }
                             div(class="target-buttons") {
                                 button(class="button", on:click=move |_| on_create(11)) { "Target 11" }