I’ve not seen Ghost in the Shell, but the clips and trailers made it look like it was borrowing at least as much from the anime as the books - the anime is far more popular to begin with, though a large part of the first series of Stand Alone Complex was taking something from a Shirow manga and putting into the show’s context. While that was generally something from Ghost in the Shell, there’s an episode where Kusanagi and Batou fight a Guges Landmate from Appleseed, for some reason.
I just took a look at the Wiki page for Alita, and I think they’re going for book 1-3, but they’re going to make her a Motorball player instead of a Bounty Hunter? The cast list is almost all characters from the first two storylines, with some alterations. Vector, who’s played by Mahershala Ali is described as a criminal who fixes Motorball matches, but in the manga he’s more of a fence and middleman.