The average American house on a basement will have something like 40 m^3 of concrete in its foundation. If all of it could be utilized, that's still ~12kWhr of storage capacity. Nothing to be sneezed at.
That doesn't seem worth it when you can fit that amount of storage in about 20 L with lithium ion cells (think a small PC case), or something like 40 L if you used sodium ion cells, which are looking like a new alternative.
Concrete offgassing of CO2 is already a big contributor to greenhouse gasses, so I can't imagine this battery version is improving things there. You'd probably have to wire your whole basement with electrodes to even access the stored energy.
OK then, so this is incredibly far from being near any real world application
I'd disagree with that, but we certainly need more info.
There are places on Earth where 300wh would be plenty and very far away from traditional power grids. Think like remote sensing weather stations or data collection stations. So a small solar panel could power these during the day and these supercapacitors would replace a wearable battery currently in use today.
We'd need more information how these perform under various temperature and moisture conditions.
A cubic meter is just a whole lot of volume for incredibly little power. A regular 80Ah car battery has almost 4 times the power capapcity as a cubic meter of this.
Power density doesn't always matter. There are applications where space is abundant, but regular maintenance is prohibitively expensive.
In my quick example of a remote monitoring station, it may cost $10,000+ to send a helicopter out to change the 12v car battery when it dies from exposure to extreme temperatures in 5 years or less. If something like this supercapacitor can last 20+ years without every be visited, it would be more cost effective.