I can’t possibly unlock the bootloader on the xperia 10 III:
Have you enabled unlocking in the Android settings menu as per the instructions?
Are you using the latest version of the SDK platform tools for Android at SDK Platform Tools release notes | Android Developers,?
They seem to ship fastboot for Windows with the files for flashing, so that shouldn’t be needed,
Apparently sometimes it is needed.
Following this tutorial I managed somehow to unlock the phone:
Sony Xperia - How to unlock bootloader and install a custom firmware - Sony Xperia - How to unlock bootloader and install a custom firmware - Invidious