I spent some (too many) months looking into this domain so I can maybe give some context.

The astonishing improvement here is that we can compute exact flows in almost-linear time. Previous algorithms for computing almost-optimal flows in almost-linear time have been known for some time, and hence it was expected that someone would eventually find an algorithm that finds optimal flows in almost-linear time. Well, looks like it's finally here!

I've only skimmed the paper but it seems to me that the authors draw on a set of techniques established for the almost-optimal case. These come with rather enormous constants, so it is unlikely that there will be a practical implementation of this algorithm any time soon.