Add anonymous listening support and redesign web-player UI

Backend:
- Expose GET /config/playback so the frontend can detect whether
  anonymous listening is enabled without requiring auth
- Wire anonymous access through track streaming and YouTube resolve flows

Frontend:
- Allow browsing/listening without a session when the backend enables it
- Redesign Inicio, Sidebar and top bar with a new dark theme, typography,
  and layout (top bar with live quick-search, sticky/blurred on scroll)
- Populate Top música, Popular and Recomendados with real Musify +
  YouTube Music data instead of placeholders
- Various shape, spacing, color and animation refinements across the
  redesigned components

backend/Core/Musify.Application/Configuration/GetPlaybackPublicConfig.cs

@@ -0,0 +1,18 @@
+using Mediator;
+using Musify.Application.Configuration.Responses;
+
+namespace Musify.Application.Configuration
+{
+    /// <summary>Reads the parts of <see cref="PlaybackConfiguration"/> that are safe to expose to an
+    /// unauthenticated client, so it can decide whether to gate the app behind sign-in at all.</summary>
+    public record GetPlaybackPublicConfigQuery : IQuery<PlaybackPublicConfigResponse>;
+
+    public class GetPlaybackPublicConfigQueryHandler(PlaybackConfiguration playbackConfiguration)
+        : IQueryHandler<GetPlaybackPublicConfigQuery, PlaybackPublicConfigResponse>
+    {
+        public ValueTask<PlaybackPublicConfigResponse> Handle(GetPlaybackPublicConfigQuery query, CancellationToken cancellationToken) =>
+            ValueTask.FromResult(new PlaybackPublicConfigResponse(
+                playbackConfiguration.AllowAnonymousListening,
+                playbackConfiguration.AnonymousFragmentSeconds));
+    }
+}

backend/Core/Musify.Application/Configuration/Responses/PlaybackPublicConfigResponse.cs

@@ -0,0 +1,7 @@
+namespace Musify.Application.Configuration.Responses
+{
+    /// <param name="AllowAnonymousListening">Whether listeners without a session can stream music at all.</param>
+    /// <param name="AnonymousFragmentSeconds">How many seconds of a track an anonymous listener may hear.
+    /// Zero means no cap. Meaningless when <paramref name="AllowAnonymousListening"/> is false.</param>
+    public record PlaybackPublicConfigResponse(bool AllowAnonymousListening, int AnonymousFragmentSeconds);
+}