How to add my brother as POA for my father's medical care?

IMO you cannot add your brother as a POA. Your Dad needs to make that assignment. You maybe able to put brother on HIPPA forms as Dads representative. These are both questions for a lawyer. States are different in their laws.

Do you have a lawyer you work with? I would consult with the lawyer that drew up the POA to begin with.
Might even want to find out if there are any other documents that he should be added to
I think you can add him yourself as a secondary.
So it could be a joint POA or one that he can take over if something happens to you.

Check with a Lawyer in your State. An Elder Law attorney. Your Dad's estate pays for this. Often the POA who now has to act for an incompetent senior can assign others tasks such as Fiduciaries and etc. It depends upon what is written in your current POA. Read your POA and see what rights you have under it. This Question may actually be answered by phone quite inexpensively by a Lawyer. Good luck. And yes, you are correct that if no longer competent it is too late for your FATHER to do this. But you may have your brother as your second when you are not available and if something were to happen to you a Social Worker could get him quickly appointed as conservator like, by phone a Justice of the Court.
Check with your Lawyer and do update us.