EntityFramework database first => generalising timestamps

IEntity.cs

namespace SameNameSpaceAsAutoGeneratedDbContext
{
  public interface IEntity
  {
    int Id { get; set; }
    DateTime CreatedAt { get; set; }
    DateTime? UpdatedAt { get; set; }
    DateTime? DeletedAt { get; set; }
  }
  
  public partial class Customer : IEntity {}
  public partial class Product : IEntity {}
}

MyDbContext.cs

namespace SameNameSpaceAsAutoGeneratedDbContext
{
  public partial class MyDbContext
  {
    public override Task<int> SaveChangesAsync()
    {
      AddTimestamps();
      return await base.SaveChangesAsync();
    }
    
    private void AddTimestamps()
    {
        var entities = ChangeTracker.Entries().Where(x => x.Entity is BaseEntity && (x.State == EntityState.Added || x.State == EntityState.Modified || x.State == EntityState.Deleted));

        foreach (var entity in entities)
        {
          switch(entity.State)
          {
            case EntityState.Added:
              ((BaseEntity)entity.Entity).CreatedAt = DateTime.UtcNow;
            break;
            case EntityState.Modified:
              ((BaseEntity)entity.Entity).UpdatedAt = DateTime.UtcNow;
            break;
            case EntityState.Deleted:
              (BaseEntity)entity.Entity).DeletedAt = DateTime.UtcNow;
            break;
          }
        }
    }
  }
}