“awareness”, as it is called in StarCraft II, is definitely a skill that improves with training.
Seasoned players remain aware of what other tasks must also be done while they are devoting attention to one and thus allocate their attention better.
I personally never had the panic freezes that some new players have in this game, but I did remember having them in StarCraft I at the initial stages, but as I improved I indeed became more aware.
Brain scans of StarCraft II players at high level also indicated that they actually play large parts of the game not with higher, cognitive function, but with lower brain functions which is another thing that improves with training that the article speaks of in terms of cognition, becoming better at it entails assimilating more and more actions into autonomous reactions allowing for better multi tasking, which certainly also reflects upon cooking and computer tasks when many of the actions become more autonomous.
That rings some bells. My observation is that I did not get better at switching, but once I’ve got used to timings of building/preparing something, it greatly reduced the anxiety for not getting things in sync, which in turn removed a decision paralysis (a bit), which kicks in even if I have a plenty of time to plan ahead. I still have trouble with remembering to adjust macro when apm has to be retained at high marks.