You're correct: CDA 230 doesn't apply to stuff the platform itself creates, so I'm not sure why you'd raise it here.
As to "promotion": what liability would arise from promoting something "hateful and false." Neither hate nor falsity are illegal (indeed, both are protected by the First Amendment). Removing 230 protections for "hateful and false" speech wouldn't actually make platforms civilly liable for it, because there is no liability for it.