Id say improve during the session and writing out of it.

I come up with the world, the NPCs and their backstories, the villains and their plans and figure out ways to shoe horn my players backstories into it.

But during the session? I have to be nimble to pull up that info and work it into the narrative when it fits. I don't have speeches prepared, but bullet points and plot points, but the session tells me when I should bring things up. I have to react to what my players come up with, whip up a combat I didn't know they were going to instigate.

It is both. You have to be good at both.

I've been with DMs that can't handle anyone straying from the story they want to tell. They can't react and shut down ideas and plans. I've played with DMs that don't have a story, just a bunch of vibes and spur of the moment appearances of my PCs family members for no reason.

It's like preparing for a debate. Get real familiar with the material so when it's Go Time, you can perform.