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.Api/Authentication/AuthenticationExtensions.cs

@@ -0,0 +1,31 @@
+using Microsoft.AspNetCore.Authentication.JwtBearer;
+using Microsoft.Extensions.Options;
+
+namespace Musify.Api.Authentication;
+
+public static class AuthenticationExtensions
+{
+    public static IServiceCollection AddAuthenticationConfiguration(
+        this IServiceCollection services,
+        IConfiguration configuration)
+    {
+        services
+            .AddOptionsWithValidateOnStart<AuthenticationConfiguration>()
+            .Bind(configuration.GetRequiredSection(AuthenticationConfiguration.SectionName))
+            .ValidateDataAnnotations();
+
+        services.AddSingleton(serviceProvider =>
+            serviceProvider.GetRequiredService<IOptions<AuthenticationConfiguration>>().Value);
+
+        services.AddScoped<JwtBearerEventsHandler>();
+        services.ConfigureOptions<JwtBearerOptionsSetup>();
+
+        services
+            .AddAuthentication(JwtBearerDefaults.AuthenticationScheme)
+            .AddJwtBearer();
+
+        services.AddAuthorization();
+
+        return services;
+    }
+}