When should I copyright my code if a startup is already using it daily?

Copyright is automatic for the person that wrote it but if you are getting paid to code it then it belongs to the startup unless you have a special arrangement. In some cases, even work done on your own belongs to them. Unless you work out an agreement that says otherwise.

BTW, copyright is only important if you are willing to defend it in court. Yes, you have the right but unless you go to court to stop its use by someone else then people will use it even if they don't have the right. The right is only enforced by suing the offender. And that takes lots of money and time in most cases.