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/api.rs

@@ -22,9 +22,22 @@ pub async fn me() -> Result<Option<User>, String> {
     resp.json().await.map(Some).map_err(|e| e.to_string())
 }
 
-pub async fn create_game(target_score: i32) -> Result<GameView, String> {
+/// Fetch the card games the platform can host (for the creation dropdown).
+pub async fn game_types() -> Result<Vec<GameTypeInfo>, String> {
+    let resp = Request::get("/api/game-types")
+        .send()
+        .await
+        .map_err(|e| e.to_string())?;
+    if !resp.ok() {
+        return Err(server_error(resp.status()));
+    }
+    let page: GameTypesPage = resp.json().await.map_err(|e| e.to_string())?;
+    Ok(page.results)
+}
+
+pub async fn create_game(game_type: &str, target_score: i32) -> Result<GameView, String> {
     let resp = Request::post("/api/games")
-        .json(&serde_json::json!({ "target_score": target_score }))
+        .json(&serde_json::json!({ "game_type": game_type, "target_score": target_score }))
         .map_err(|e| e.to_string())?
         .send()
         .await