Very well written. Our brain CANNOT do two things at once. Not two things that require cognitive processes for sure.
However, trying to do two really unrelated things at once even if they don’t make sense and you screw both up, can help strengthen your neural networks by giving your brain additional workload. Eg, watching a movie in a non native language on half a screen while writing an article on the theory of relativity.
These don’t use the same sensory systems at least. One uses ears and eyes primarily, it isn’t something you’re producing, it’s something you’re creating. The other uses your brain and fingers. It’s kind of like gymming but for the brain.