Is there a way to move apps into different categories in the App Library if the auto sorting doesn’t make sense?
on the iPhone 13, is there a way to move apps in the App Library to different categories if the auto sort doesn’t make sense?
No, that is not an option. You can let Apple know it's a feature you'd like to see here:
Meanwhile, you can create your own folders and arrange your apps in the way that makes sense to you.
Move apps and create folders on your iPhone, iPad, or iPod touch - Apple Support