I absolutely can't multitask: I can't drive properly and talk (I can do it, but my driving isn't good). I could never talk and play piano, nor even sing along as I played (I don't have opportunity to play anymore).

I can however talk and type, but it's done in a way where I fill a mental register with the sentence I'm typing, switch focus whilst my hands operate on that register; then fill the register in a pause from the conversation. It's just rapid task switching for me except the typing. Probably took me a decade of touch typing to get there.

I'm also I've of those people who ends up writing down the conversation if I'm handwriting and conversing.

-- reflecting now when playing piano I'd try and fill a mental register with the forthcoming musical phrase whilst I switched to speaking. I think perhaps it didn't work because I struggle with rhythm and so need central focus to maintain any semblance of rhythm.

No.

Why not? Parent raises a good point, how do we define a single task?

If you are playing one melody with your left hand on the piano and one with your right, is that one task or two?

Because everything but the executive task flow is being handled via processes known as automaticity.

https://en.wikipedia.org/wiki/Automaticity

We don't have a definitive diagram of the mind to point to, but I feel we all really can feel what is and what isn't multitasking.

Once internalized through experience, hand movements on piano (or computer) keyboard are subconscious. They don't tax your brain. Thinking about what you're playing/writing and why are you doing it is still within one "context of execution". They are closely related mental activities sharing most of the same data. Starting to simultaneously think about or engage in an unrelated, cognitively demanding activity - this is multitasking, or the so-called "context switch".