The paper just says "an estimated energy density of >1 kW/m^2"

"Energy density" is a misnomer, it should be power density, since the kW is a unit of power (rate of energy generation), not energy.

That's quite an amount, about 3-5x the amount of energy generated by solar cells of the same surface area. It would mean the device would generate $2000-$4000 on a yearly basis.

Didn’t it say cubic meter, not square?

Nope.

Watts are a rate of one joule per second.

If you want to talk about a quantity of energy rather than a rate of energy production/consumption, the units would be either kilowatt hours or joules (1 kWh = 3,600,000 joules).

Yup, kilowatt hours are a cursed unit that simply reduces to joules (a nice and easy to remember 3.6 million of them).

Yeah I have to work that out every time