Can I switch mi 13 ultra from hyper os eu to global with unlocked bootloader.?


Yes but do not lock your bootloader unless your device is a global version or you will brick it. You will have to format data ( reset it ) due to possible partition differences.
Use scripts to flash, if you really have to use miflash, make sure you untick the lock bootloader setting before flashing. If you do lock it and it becomes a brick in edl mode, only a paid service will get it back. You will know it's in edl as it is detected on your pc but you will not have fastboot or recovery.