Any updates on this.
After installing KB5124008, i have the exact same problem with File History. And the "Reconnect the drive" message.
Have even tried with a fresh SSD drive and renaming Configuration and Data directories on the PC, then selected the new drive in File History, and it will create fresh Configuration and Data directories on both the external SSD and the PC, so it can for sure see the drive. Then Run backup and l get the same message to Reconnect the drive. So this is clearly broken !