A normal backup (via Finder or iCloud) will back up all app data. Of course, Apple doesn’t provide a means to restore data for just one app - you need to restore the entire device to restore from these backups.
iMazing offers finer-grained control. You can back up and restore single apps. And the last time I used it (many years ago), it could also read and restore data from a locally-stored Apple backup (you’ll need the backup’s password if it is encrypted).
Of course, if the app’s data is corrupt, then restoring it will restore the bug as well.
If, however, News+ stores data on a cloud server (I don’t know, I don’t use it), then a full delete/install should pull your data back down from that cloud server. Whether this is all of your data or just some data (e.g. subscribed sources and the list of articles you’ve already read), is something I don’t know - someone with more knowledge will have to chime in on that.