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.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

backend/Musify.Infrastructure/Persistence/DatabaseDesignTimeFactory.cs

@@ -0,0 +1,29 @@
+using Microsoft.EntityFrameworkCore;
+using Microsoft.EntityFrameworkCore.Design;
+using Microsoft.Extensions.Configuration;
+using Musify.Infrastructure.Configuration;
+
+namespace Musify.Infrastructure.Persistence
+{
+    public class DatabaseDesignTimeFactory : IDesignTimeDbContextFactory<Database>
+    {
+        public Database CreateDbContext(string[] args)
+        {
+            var configuration = new ConfigurationBuilder()
+                .SetBasePath(Directory.GetCurrentDirectory())
+                .AddJsonFile("DesignSettings.json")
+                .AddUserSecrets<DatabaseDesignTimeFactory>()
+                .Build();
+
+            var databaseConfiguration = configuration
+                .GetRequiredSection(DatabaseConfiguration.SectionName)
+                .Get<DatabaseConfiguration>()
+                ?? throw new InvalidOperationException($"{DatabaseConfiguration.SectionName} configuration section not found.");
+
+            var optionsBuilder = new DbContextOptionsBuilder<Database>();
+            optionsBuilder.UseNpgsql(databaseConfiguration.ConnectionString);
+
+            return new Database(databaseConfiguration);
+        }
+    }
+}