Studies I've seen are not so clear that an EMP would kill many satellites. They would raise radiation levels 10x over normal for few months, but most Starlink satellites would be fine (as seen in the last solar CME event).
It took out 3 satellites initially (there were very few at the time)
> In the months that followed, these man-made radiation belts eventually caused six or more satellites to fail
Today, with modern nukes, if one was intentional, they could disrupt or destroy the space ecosystem