I’ve had a problem with a black screen after the Android 13 update too. It would still let me unlock the phone and access the quick settings menu though.
And I was able to fix my black screen.
I went into the phone’s settings via the quick settings menu, went to the apps and launched the Play Store from there.
I installed an alternative Android Launcher (XOS Launcher in my case) in the hope to have a workaround until there is a solution found that doesn’t reset the phone.
The Launcher worked, but when I accidentally closed it, I noticed that the phone’s launcher worked again too.
I’m not really knowledgeable with how a smartphone’s OS works, so I can’t tell you exactly how that fixed the bug.
Hope I was able to help someone with the same problem.