Refactor and clean up codebase:

- Introduced `IGameRepository` interface and its implementation.
- Transitioned namespaces to `file-scoped` for consistency.
- Simplified class definitions, e.g., `Game` and `SixDigitInt`.
- Restructured `GameField` logic for improved readability and functionality.
- Fixed formatting issues in `API.csproj` and added a `using` directive in `Program.cs`.

API/Services/GameManager/IGameManager.cs

@@ -1,8 +1,7 @@
-namespace API.Services.GameManager
+namespace API.Services.GameManager;
+
+public interface IGameManager
 {
-    public interface IGameManager
-    {
-        public int CreateGame(string playerName);
-        public bool JoinGame(string playerName, int gameCode);
-    }
-}
+    public int CreateGame(string playerName);
+    public bool JoinGame(string playerName, int gameCode);
+}