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/AuditableEntityInterceptor.cs

@@ -0,0 +1,43 @@
+using Microsoft.EntityFrameworkCore;
+using Microsoft.EntityFrameworkCore.Diagnostics;
+using Musify.Domain.Abstractions;
+
+namespace Musify.Infrastructure.Persistence
+{
+    public sealed class AuditableEntityInterceptor : SaveChangesInterceptor
+    {
+        public override InterceptionResult<int> SavingChanges(DbContextEventData eventData, InterceptionResult<int> result)
+        {
+            ApplyTimestamps(eventData.Context);
+            return base.SavingChanges(eventData, result);
+        }
+
+        public override ValueTask<InterceptionResult<int>> SavingChangesAsync(
+            DbContextEventData eventData, InterceptionResult<int> result, CancellationToken cancellationToken = default)
+        {
+            ApplyTimestamps(eventData.Context);
+            return base.SavingChangesAsync(eventData, result, cancellationToken);
+        }
+
+        private static void ApplyTimestamps(DbContext? context)
+        {
+            if (context is null)
+                return;
+
+            var now = DateTime.UtcNow;
+
+            foreach (var entry in context.ChangeTracker.Entries<IAuditable>())
+            {
+                if (entry.State == EntityState.Added)
+                {
+                    entry.Entity.CreatedAt = now;
+                    entry.Entity.UpdatedAt = now;
+                }
+                else if (entry.State == EntityState.Modified)
+                {
+                    entry.Entity.UpdatedAt = now;
+                }
+            }
+        }
+    }
+}