I got the update today on my unlocked version of the S21 ultra here in the UK. Initially, the update annoyed me as my phone was stuck in a reboot/restart loop. I realised why my phone kept restarting (stuck in a restart loop) after the update was due to some buggy apps. Android 13 also warned of these apps and tried to deny permission for these apps, which I ignored, unknown to me. These apps were the culprits of why my phone kept restarting. After fifteen minutes of wishing I hadn't updated my phone, I revisited those apps android 13 warned me about.
It's been beautiful since then; Android 13 on the S21 runs quite smoothly after those apps were deleted and the cache cleared.
I saw some posts here about phones stuck in a restart loop; sometimes, this is due to some buggy apps, and on first updating the operating system, Android 13 must have warned you of those apps. Please revisit some of those apps, delete them, and you will have a fun Andriod 13 on your devices.
These are apps that I downloaded off the Web and not on the playstore. Galaxy MaxHz was one. Like I said, look for apps on your phone that you've been warned about. Apps you have on your phone might not be the ones I have on my phone.