A charged battery is merely an imbalance of electrons. It's like a stored water power system. You put water in a reservoir on the top of the hill and open the tap and let it run into the reservoir at the bottom. When the upper reservoir is empty, your system still has as much water as it did before it just has no potential to generate power until you pump it back up the hill.

What they're saying is that the electrons captured to change the state in a solid-state drive holds physical mass. If this mass change is extrapolated to the data storage of the entire internet, then it physically ways as much as a strawberry.

This likely means that all recorded data in human history would weigh less than your standard package of printer paper from Staples.