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/Program.cs

@@ -1,3 +1,4 @@
+using API.Controllers;
 using API.Services.GameManager;
 
 var builder = WebApplication.CreateBuilder(args);
@@ -28,8 +29,8 @@ app.UseStaticFiles();
 app.UseAuthorization();
 
 app.MapControllers();
-app.MapHub<API.Controllers.GameHubSocket>("/api/gamehub");
+app.MapHub<GameHubSocket>("/api/gamehub");
 
 app.MapFallbackToFile("index.html");
 
-app.Run();
+app.Run();