What’s the downside here? Lithium ion batteries have an energy density of 150-350 Wh/kg, so this is firmly at the bottom of that range.

Naive, back of the napkin is 446 kWh / m^3. There’s a lot of content out there!

I haven't read the paper in detail yet but the easiest way to cheat is to calculate the density of a single layer, "capacitor plate" or surface or whatever it is that the microbes are living on and consider the "structural" cement as not counting towards the density calculation because theoretically speaking, there could be a manufacturing method to make a cement that creates the promised surface area even though such a process would be completely impractical to commercialise.

"Sorry the power is out - the concrete got sick".

And ensuring electrode integrity is probably quite fiddly during construction and maintenance is presumably also fiddly.