50 GW for 1s is 50GJ. If that’s the energy delivered in a year then the average power is 1.584 kW. As long as your power plant lasts a few years or more (and you can actually put that energy onto the grid), the average power is a useful quantity to compare against any other power generation. Saying the average is over a period of a year doesn’t express anything about the variability of the power; just like saying your power plant could power a single electric heater running continuously, for a year, a decade or whatever period you like.

Power per unit time is kind of nonsense. It expresses an increase or decrease in power. Energy per unit time is power and is how we typically rate things that make or consume energy.