Device name : Xiaomi 13 Pro
Codename : nuwa
Speed up tips : All methods have been fixed, the end.
Bootloader : You need to unlock the bootloader if you want to flash a rom into your phone via fastboot method, and your data could be deleted as you choose, please make sure you have backed up your personal data.Apply for Bootloader Unlock here.
MIUI Rom : Yes , go to the MIUI site: Xiaomi 13 Pro(nuwa) - MIUI Official ROMs