Samsung already released the Android 13 updates for locked Galaxy S21 models in the US. The previous update was for the Galaxy S21 phones locked to different carriers. Now, Samsung also released the Android 13 update for unlocked phones.
The new update comes with firmware version G99xU1UEU5DVK3 and brings One UI 5.0 to the phones. It still uses the October 2022 security patch instead of the more recent November 2022 patch.
How to install Android 13 ( One UI 5.0) on Galaxy S21?
If you are using an unlocked Galaxy S10, you can update your phone by going to Settings » Software update. Then tap on Download and install.