refactor(api): OpenAPI response metadata, cached user sync, ProblemDetails

- Document every endpoint's responses (Produces<T>/status codes/validation)
  so the generated OpenAPI/Scalar docs carry response schemas and status codes
  instead of empty responses
- Cache recently-synced user ids (IMemoryCache, 15 min) in the JWT
  TokenValidated handler so user provisioning no longer hits the DB on every
  authenticated request
- Add ProblemDetails + UseExceptionHandler for consistent RFC7807 errors
- Add ToCreatedResult ErrorOr helper and use it in the create endpoints
- Normalize the playlists route to lowercase (/playlists)

Verified: booted the Api against RabbitMQ + Postgres in Docker and inspected
/openapi/v1.json — operations now expose response schemas/status codes and the
route is /playlists.

Build: 0 warnings, 0 errors.

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

backend/Musify.Api/Authentication/JwtBearerEventsHandler.cs

@@ -1,12 +1,18 @@
 using Mediator;
 using Microsoft.AspNetCore.Authentication.JwtBearer;
+using Microsoft.Extensions.Caching.Memory;
 using Musify.Application.Users;
 using System.Security.Claims;
 
 namespace Musify.Api.Authentication;
 
-public sealed class JwtBearerEventsHandler(IMediator mediator, ILogger<JwtBearerEventsHandler> logger) : JwtBearerEvents
+public sealed class JwtBearerEventsHandler(
+    IMediator mediator,
+    IMemoryCache cache,
+    ILogger<JwtBearerEventsHandler> logger) : JwtBearerEvents
 {
+    private static readonly TimeSpan UserSyncCacheTtl = TimeSpan.FromMinutes(15);
+
     public override async Task TokenValidated(TokenValidatedContext tokenValidatedContext)
     {
         var principal = tokenValidatedContext.Principal!;
@@ -18,6 +24,10 @@ public sealed class JwtBearerEventsHandler(IMediator mediator, ILogger<JwtBearer
             return;
         }
 
+        var cacheKey = $"user-synced:{userId}";
+        if (cache.TryGetValue(cacheKey, out _))
+            return;
+
         var username = principal.FindFirstValue(ClaimTypes.Name)
             ?? principal.FindFirstValue("preferred_username")
             ?? principal.FindFirstValue(ClaimTypes.Email)
@@ -32,6 +42,8 @@ public sealed class JwtBearerEventsHandler(IMediator mediator, ILogger<JwtBearer
             await mediator.Send(
                 new SyncUserCommand(userId, username, firstName, lastName, profilePictureUrl),
                 tokenValidatedContext.HttpContext.RequestAborted);
+
+            cache.Set(cacheKey, true, UserSyncCacheTtl);
         }
         catch (Exception exception)
         {