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.Infrastructure/Persistence/DatabaseDependencyInjection.cs

@@ -0,0 +1,27 @@
+using Microsoft.Extensions.Configuration;
+using Microsoft.Extensions.DependencyInjection;
+using Microsoft.Extensions.Options;
+using Musify.Application.Contracts;
+using Musify.Infrastructure.Configuration;
+
+namespace Musify.Infrastructure.Persistence
+{
+    public static class DatabaseDependencyInjection
+    {
+        public static IServiceCollection AddDatabase(this IServiceCollection serviceDescriptors, IConfiguration configuration)
+        {
+            serviceDescriptors
+                .AddOptionsWithValidateOnStart<DatabaseConfiguration>()
+                .Bind(configuration.GetRequiredSection(DatabaseConfiguration.SectionName))
+                .ValidateDataAnnotations();
+
+            serviceDescriptors.AddSingleton(serviceProvider =>
+                serviceProvider.GetRequiredService<IOptions<DatabaseConfiguration>>().Value);
+
+            serviceDescriptors.AddDbContext<Database>();
+            serviceDescriptors.AddScoped<IDatabase>(serviceProvider => serviceProvider.GetRequiredService<Database>());
+
+            return serviceDescriptors;
+        }
+    }
+}