A battery is a source.

a battery is not a source for power just a storage device. A battery
can't
generate it's own power.

Of course it can. A battery, just like any other source, converts one form
of energy into electrical energy. Power is the time rate of energy.

A battery doesn't "store charge". It stores energy. There's an energy
transduction process that you're intentionally ignoring. If you were to
prevent the battery from performing the necessary chemical reactions to
generate charge (perhaps by manipulating the temperature), you wouldn't have
a charge. The same cannot be said of a capacitor, whose sole job is to
store charge.