chore: group .NET into backend/ and drop non-.NET test artifacts

- Move all .NET (6 projects, solution, Directory.*.props, nuget.config)
  into backend/ so the monorepo root can host non-.NET projects later
- Remove throwaway test artifacts: player.html, pl.json
- Trim dead Flutter rules from .gitignore

Build from backend/Musify.slnx: 0 warnings, 0 errors.

backend/Musify.Api/Extensions/ServiceCollectionExtensions.cs

@@ -0,0 +1,34 @@
+using FluentValidation;
+using Musify.Infrastructure.MassTransit;
+using Musify.Infrastructure.Persistence;
+using Musify.Application.Configuration;
+using Musify.Infrastructure.Services;
+using Musify.Api.Authentication;
+using Musify.Api.DataTransferObjects.PlayLists;
+using Musify.Api.OpenApi;
+using Musify.Api.Scalar;
+
+namespace Musify.Api.Extensions;
+
+public static class ServiceCollectionExtensions
+{
+    public static IServiceCollection AddApplicationServices(this IServiceCollection services, IConfiguration configuration)
+    {
+        services.AddDatabase(configuration);
+        services.AddApplicationStorageConfiguration(configuration);
+        services.AddPlayListConfiguration(configuration);
+        services.AddTrackConfiguration(configuration);
+        services.AddStreamGatewayConfiguration(configuration);
+        services.AddStorageService(configuration);
+        services.AddStreamTicketService(configuration);
+        services.AddUploadIntentConfiguration(configuration);
+        services.AddMassTransitClient(configuration);
+        services.AddMediator();
+        services.AddAuthenticationConfiguration(configuration);
+        services.AddOpenApiConfiguration();
+        services.AddScalarConfiguration();
+        services.AddValidatorsFromAssemblyContaining<CreatePlayListRequest>();
+
+        return services;
+    }
+}