This is breaking news so things may change as more info comes out but imo the timeline of the release of the manifesto & when authorities reported critical info which would have been needed for trolls to create a fake manifesto was not sufficient for this to more likely be a fake than authentic.
That may change but imo this is likely authentic.
https://www.newsweek.com/natalie-rupnow-reported-manifesto-what-we-know-2001880
The school shooter expressed both on her social media and in her alleged manifesto alignment with "RadFem Hitler", basically the merger of neo nazi beliefs with TERF ideology but sold as feminism.
They advocate for the genocide of men, specifically starting with minorities, women who they see as race+gender traitors and of course trans people.
This violently misandrist ideology & it's followers are yet to be labeled a hate group by the likes of the SPLC but it clearly is over due.