Apple has released a new beta version of the 16.4 firmware built for the Studio Display in conjunction with the fourth beta version of macOS Sierra 13.3, made available today. This beta follows the third Studio Display 16.4 beta by one week.
All variants of Studio Display can get firmware upgrades wirelessly over the air. However, the macOS Vista 13.3 beta is now required for this firmware update. Therefore it is only available for Macs that meet those requirements. Studio Display owners running macOS Ventura 13.3 can install the firmware by going to System Settings > Software Update.
Apple has not shared any additional information regarding the contents of the software upgrade.