How to multitask when you’re wired for deep work

I need to get better at multitasking.
This feedback, which I received a few weeks ago, came as a bit of a surprise. Mainly because, for a long time, I have been practising the opposite, trying instead to perfect the art of focusing on whatever task I feel is most important and blocking out distractions. I’m pretty good at this. I find it relatively easy to tunnel in on something, enter into a flow state, and ignore pretty much everything else.
I even consider this to be a gift. Other people complain about being unfocused and easy to distract. I am not.
But what helps me perform well at tasks like writing or coding is, possibly, not such a good thing for managing — a responsibility I am now grappling with.
As my focus has turned from my own output to the output of my team, I realise — and have been told — that being available to my team and keeping multiple plates spinning at once is now the priority. If a member of my team is blocked, it’s my responsibility to unblock them quickly. If there’s a (metaphorical) fire that needs putting out, it’s my job to fix the problem or find someone else who will.
But what does multitasking actually mean? Can it be learned? Is it really something worth sacrificing deep…