So again, kWh is accurate. When you're talking about batteries, kWh refers to the storage capacity of the battery. How much you pay for electricity at your house isn't relevant.

And if you don't believe me, you can look at the papers I cited from experts, who also use kWh:

https://www.cell.com/joule/fulltext/S2542-4351(19)30300-9https://www.nrel.gov/docs/fy21osti/79236.pdf

Also note that in the chart when I am talking about the cost of electricity, then I use MWh.