To anticipate an objection, I would agree that the competence of both tasks diminishes somewhat. However the overall competence of both is sufficient.
My brain also seems capable of detecting when more attention is required, and automatically stopping the lower priority task. For example, if I had to quickly merge across many lanes on a busy freeway, then I would likely cease conversation during that maneuver. I don’t have to think too much about this consciously. The brain understands that driving is paramount and it will automatically preempt anything lower priority when more cognitive attention is required.
I would be interested to know what the research says about phenomena like that. There must be research like this supporting aviation, space flight, and nautical activities.
It seems easiest to multitask across different modes, e.g., I can work with my hands or drive a car while listening to an audiobook. I can have a social conversation with friends over voice chat while playing a video game.
Maybe the degree to which you can multitask depends upon the type of task and to what extent your brain can perform it automatically. The rote tasks involved in driving for example require very little attention to perform safely and correctly.