For anyone else that attempts to update the firmware using Windows 11 and soft-bricks their device (like me), the issue is caused by the WMIC command being missing (and its underlying components) as they're no longer installed in Windows 11 by default.
Installing those components via Window's Optional Features (I used this guide:
Install WMIC on Win11) and then attempting the firmware flash via FLASH.BAT again brought me back to a working device.
It might be nice for Airspy to either note in their README (in BIG CAPITAL LETTERS) that firmware updates via Windows 11 are specifically not supported, or if the above is the official fix, to suggest that in their readme. Having those components autoinstalled via the flash.bat script might also be an option.