It sounds like the energy capacity and power output can be scaled independently of one another. But as this article is meant for a wide audience, I think they simplified the discussion by making some assumptions about the desired power output per kWh stored.

Not unreasonable. The details are always in the research paper after all.

Your max power output probably doesn't go up ny "just making the tank larger"?

kWh does not measure max power, it measures capacity. A kWh is a constant factor multiple of Joules. I’d think you could absolutely make the capacity larger (ie store more energy) by just making the tanks larger. The flow rate is the thing that seems to determine the power output.

Yes, but I wasn't talking about capacity. I was talking about max output power.

Increasing the size of the tanks to increase the energy storage capacity, without increasing output power would be... useless.

Extreme example: a huge expensive 100 MWh battery that you can only draw a max power of 100 W from = useless.