Samsung Sm-s908u update

AT&T is well known for not allowing manufacturers to release updates for its carrier version devices.  They instead provide the updates directly to AT&T to distribute the update only over their network. They do this to try and discourage customers leaving and using their devices on other networks.

You can try removing your SIM, putting the device on WiFi, and checking for updates to see if it shows up for you.  If not, I would highly re commend visiting XDA's S22 Ultra forum and follow the tutorials to convert your device to the U1 (US non-carrier specific) firmware or to the TMK (Metro) firmware.  Doing this would ensure you get updates and would also make your device fully compatible with T-Mobile's network.