The backup only contains data and settings. No part of the OS is included in the backup. So restoring a backup won’t restore a corrupted OS. However, resetting the phone won’t fix a corrupted OS either, as the phone reset simply removes all of the data and settings and leaves the OS in place.
iOS is pretty robust, so it’s unlikely that you have a corrupt OS. If you really think it’s a corrupt OS then the way to fix that is to put your phone in DFU mode and connect it to a computer and allow it to reinstall the OS, but I don’t think that’s going to be necessary in this case.
I think more likely you may have a corrupt configuration or corrupt data of some sort and that may or may not get restored with a backup. It’s possible that the system may notice and remove the corruption during the backup or restore process, or it’s possible that the corruption will get restore. That’s kind of the thing about corruption… you don’t really know how the system will handle it, since it’s not supposed to be that way.
I think calling apple may be the best option, since it’s possible that they have run into this before and have a solution for it. If you didn’t want to do that, then I might try the following…
1 - Make sure you have a good backup, then reset the phone and set it up as a new phone without restoring a backup and try the news app again. If it works now, then it’s likely the OS is good. If it still doesn’t work, then try to put the phone in DFU mode and connect it to a computer to reinstall the OS, then try to set up the phone without restoring a backup again and see if it works now.
2 - If you can get it to work when you set up the phone without restoring a backup, then reset the phone again and restore your backup and try it again. If it works, great. The backup/restore process may have removed any corruption. If it doesn’t work now, then you may need to work with apple to get it fixed, or reset the phone again without restoring your backup and reconfigure it.