If a backup QB has to be announced, I think it will be Haener as he is more "seasoned" than Rattler as to give Rattler more time to get accustomed to being a professional week in and week out.
For what it's worth, Haener is listed second team on the team website, so at least for now it looks like he'd be the first man up. And I think your rationale is correct, in that Rattler isn't ready for that responsibility yet.
But at the same time, what seasoning does Haener really have, and between the two, does a year carrying a clipboard on gameday and running the scout team really make up for him only being able to make a fraction of the throws that Rattler can make?
I haven't seen anything from Haener that has suggested there's anything special about him, and wouldn't be opposed to letting him go in favor of a veteran backup, with Rattler filling the project/prospect role that Haener filled last year. But Carr has also been a pretty durable quarterback throughout his career, so maybe the whole backup question is moot.