There is an Italian thread where a user claims that the problem comes from a factory reset which will lock your device to the July 1 update since it would erase previous updates, or an upgrade from Android 12 to 13 will lock your device to whatever system update was installed before the upgrade.
Support said that making an error report on the Samsung Members App and sending a system log is the only way to address the issue and get a proper response. Maybe if some of you do this, they'll try to fix the problem.
Unfortunately, when I bought my new Samsung phone in November, the initialization crashed and wouldn't progress, so I had to do a factory reset, and then did an immediate upgrade from 12 to 13. That was when I first noticed that I was stuck on July 1.