Samsung S21 Ultra Android 13 When?

You can always sideload the update if you don’t want to wait…  Just download the update put it on your device and load it through recovery.  It won’t touch the carrier partition and everything should work.  If there are bugs that happens when it does then it may be the reason for delaying the update which the OEM has to fix.

Also Samsung pushed it for some devices but not all devices.  There’s a difference…  Each carrier, and country has different requirements to meet before it’s officially pushed for those specific devices.  I won’t go into full detail about it.  It’s been explained decades ago, but no one listens to it.  Carriers don’t have control like people in the USA think they do.