SEARCH-1: separator-insensitive NameSearch + OriginBreeder (Herkunft) filter

- Gerbil.NameSearch (lowercase, strip whitespace/.-_) auto-synced in ApplicationContext
  .SaveChanges; Gridify-filterable so 'clan kleine chaoten' matches 'Clan-Kleine-Chaoten'
  (client strips separators the same way). GerbilSearch.Normalize shared helper.
- Gerbil.OriginBreeder (free-text Herkunft) on DTO+Input, set by the FEAT-8 import from the
  source Zucht (imported animals have no OriginContact). Gridify-filterable.
- GET /gerbils/breeders: distinct non-empty OriginBreeder values for the Herkunft dropdown.
- Migration AddSearchFields (+ NameSearch backfill SQL for existing rows).

GerbilManagerWebAPI/ApplicationContext.cs

@@ -18,6 +18,29 @@ public class ApplicationContext : DbContext
     public DbSet<SaleContract> SaleContracts => Set<SaleContract>();
     public DbSet<BreederSettings> BreederSettings => Set<BreederSettings>();
 
+    // Keep Gerbil.NameSearch in sync on every save (separator-insensitive search key),
+    // so it can never drift from Name regardless of which code path mutates the entity.
+    public override int SaveChanges(bool acceptAllChangesOnSuccess)
+    {
+        SyncNameSearch();
+        return base.SaveChanges(acceptAllChangesOnSuccess);
+    }
+
+    public override Task<int> SaveChangesAsync(bool acceptAllChangesOnSuccess, CancellationToken cancellationToken = default)
+    {
+        SyncNameSearch();
+        return base.SaveChangesAsync(acceptAllChangesOnSuccess, cancellationToken);
+    }
+
+    private void SyncNameSearch()
+    {
+        foreach (var entry in ChangeTracker.Entries<Gerbil>())
+        {
+            if (entry.State is EntityState.Added or EntityState.Modified)
+                entry.Entity.NameSearch = GerbilSearch.Normalize(entry.Entity.Name);
+        }
+    }
+
     protected override void OnModelCreating(ModelBuilder modelBuilder)
     {
         modelBuilder.Entity<Gerbil>(e =>