If you see a black screen after updating, try deleting the game (and its old data) and performing a clean reinstall of the base game followed by the update.
Install the first, then boot it once to generate a clean save state. triangle strategy switch nsp update work
The update requires a higher Horizon OS (Switch Firmware) version than what is currently installed on your EmuMMC/SysMMC. If you see a black screen after updating,