Fix integration tests - shared database across test classes

- Update CustomWebApplicationFactory to use static database name
- Ensure all tests share the same in-memory database instance
- This fixes authentication flow tests where registration must persist for login
- All 12 integration tests now pass

tests/integration/backend/IntegrationTestBase.cs

@@ -12,6 +12,9 @@ namespace backend.Tests.Integration;
 
 public class CustomWebApplicationFactory : WebApplicationFactory<Program>
 {
+    // Use a static database name so all tests in the same process share the database
+    private static readonly string _databaseName = $"IntegrationTestDb_{Guid.NewGuid():N}";
+    
     protected override void ConfigureWebHost(IWebHostBuilder builder)
     {
         builder.ConfigureServices(services =>
@@ -26,10 +29,10 @@ public class CustomWebApplicationFactory : WebApplicationFactory<Program>
                 services.Remove(descriptor);
             }
 
-            // Add in-memory database
+            // Add in-memory database with consistent name
             services.AddDbContext<RacePlannerDbContext>(options =>
             {
-                options.UseInMemoryDatabase(Guid.NewGuid().ToString());
+                options.UseInMemoryDatabase(_databaseName);
             });
         });
     }