I just found a brand new Longwell E344534 power cord and wondering if/why I should keep it?

I believe this is a extension cord for the older Apple power adapters, and as such, should you have (or ever need) to use it with these adapters, it will come in handy.

Your 2013 MacBook should have come with this type of adapter and this cord could be used with it.

That's commonly called a “duckhead” power cord, in Apple jargon. It’s still in common use.

The MacBook Pro charger brick has two plugs, either a short duckhead for direct attachment, and can be swapped for a duckhead with a cord.

Using Apple power adapters, cables, and duckheads with Apple products - Apple Support

The circled piece with the electrical contacts slides off as shown, and can be replaced with the cord.