Specifically to radio astronomy: https://en.wikipedia.org/wiki/Luminosity#Radio_luminosity
So for FRBs, we get the received brightness, and if we can measure the distance, we can use the basic inverse square scaling to estimate how much energy it had at the source. (Why inverse square? Because the area of a sphere is 4 pi R^2 - if you go twice as far away, the signal is spread out over 4 times the area, and so on.)
The key problem is a distance estimate for the FRBs - we have a pretty precise measurement for FRB 121102 because we identified its host galaxy and measured the redshift to that galaxy, so we know how far away it is. That's now been done for 2 other sources. For the rest, we can use the pulse dispersion, which measures the integrated column density of electrons along the line of sight, along with models for our galaxy and the intergalactic medium, to get some idea. It's not as good, but better than nothing.
> power the world for three centuries
Our sun for example is emitting enough energy in all directions to power the world for 300 years (over the course of 300 years), and most of it misses us.
Our sun isn't particularly impressive in terms of energy and such compared to other astro-objects, so I feel like these kinda of events releasing so much energy are to be expected.
I think you're saying any amount of energy can be produced by any amount of power, if the amount of time is unspecified. Which is true, but not substantive.
The problem is, while you can reduce the energy requirement by making the beams narrow, that increases the total number of sources by the same factor. When we say that there are between 5000-10,000 FRBs all over the sky every single day, we are referring to FRBs beamed towards us. If you apply a 10% beam, your energy requirement drops by 10x, sure, but the source count goes up by 10x.
Right now, we don't have a large enough plausible progenitor population, even at 1x, for these FRBs. It's a really fun problem.
[1] See, e.g, the Methods section in https://www.nature.com/articles/nature20797 (or https://arxiv.org/abs/1701.01098)