Maximum discharge rates for batteries are generally called "C" with units of hour^-1, though the units are often left off for some reason.

For the purposes of an installation such as this, C is essentially a constant, depending on factors such as the chemical and physical construction of the cells and thermal management system of the batteries. Given C and the maximum power output, you can calculate the actual energy capacity of the battery.

Describing capacity in terms of power rather than energy reflects its usage in actual practice. I doubt the C of the battery is higher than 1/hour, and peaker plants can be brought online on a timescale of 10 minutes or so. So if the grid has a shortfall in power, the relevant question is whether the battery has the power capacity to make up that difference. If it can, it should have the energy capacity to last until the rest of the grid brings online more supply (assuming it didn't start at a low state of charge).

The size of the expansion is 64.5MWh of battery storage and 50MW of inverters according to this source: https://www.pv-magazine.com/2020/06/23/adding-50mw-64-5-mwh-...

Really I'd expect it to be measured in both.

Megawatt hours measures how much energy it can store, megawatts measures how fast it can discharge.

The battery has a maximum safe discharge rate. I suspect the performance of a utility-scale power reserve is limited by its discharge rate, not its charge capacity. (This also makes it an apples-to-apples comparison to the peaking power plants it takes the place of.)

This is my pet peeve as well. But not being a native English speaker I figured I won't try to lecture people on this - not my language after all.

Those are not English units.