My understanding is that the empirical basis for the forecasting comes from the academic research of Phillip Tetlock, summarised in the book Superforecasting (I read the book recently, it's pretty good).
Essentially, the research signed up people to conduct large amounts of forecasts about world events, and scored them on their accuracy. The research found that certain people were able to consistently outperform even top intelligence experts. These people used the sort of techniques familiar to EA: analysing problems dispassionately, breaking them down into pieces, putting percentage estimates on them, and doing frequent pseudo-bayesian "updates". I say pseudo-bayesian because a lot of them weren't actually using bayes theorem, instead just bumping the percentage points up and down, helped with the intuition they developed, which apparently still worked.
One theory as to why this type of forecasting works so well is that it makes a forecasting a skill with useful feedback: If a prediction fails, you can look at why, and adjust your biases and assumptions accordingly.
Two important caveats that are often overlooked with this research: First, all these predictions were of bounded probability, where the question-makers estimated probability was in the range between 5% and 95%. So no million to one shots, because you'd have to make a million of them to check if the predictions were correct. Second, they were all of short term predictions. Tetlock states multiple times in his book that he thinks forecasts beyond a few years will be fairly useless.
So, if the research holds up, the methods used by EA are the gold standard in short-term, bounded probability forecasting. It makes sense to use it for that purpose. But I don't think this means that expertise in these problems will transfer to unbounded, long term forecasts like "will AGI kill us all in 80 years". It's still useful to estimate those probabilities to more easily discuss the problem, but there is no reason to expect these estimates to have much actual predictive power.
My sense is that EA overrates forecasting a bit and that the world underates it a lot.
Some underrated views I suggest:
Forecasting is more useful as a filtering tool/a personal improvement tool than as part of better decision making. I suggest that individuals would gain from playing the estimation game each month and taking the hits that reality deals, but there are many things we could do to improve ourselves and if this doesn't fit for you, fair enough.
But the idea that every org should be forecasting or that every process should involve forecasting doesn't seem to fit in reality. I still look for ways it can (maybe there is a silver bullet!) but I don't think you, the median EA should. If you want to test your knowledge of a topic, forecast on it. If you see someone has a good track record, consider taking their thoughts more seriously. Other than that, probably don't think that much more than you are interested to/you think it's important to already.
This strongly resonated with me especially after taking part in XPT. I think I set my expectation really high and got frustrated with the process and now take a relaxed approach to forecasting as a fun thing I do on the side instead of something I actively want to take part of as a community.