Thanks for the details. Since your Roon Server is running on a Mac mini, let’s first check whether macOS itself can see the drive - if the operating system can’t mount it, Roon won’t be able to read it either.
Please connect the backup drive to the Mac mini and check the following:
Open Disk Utility (Applications > Utilities). Does the drive appear in the left-hand sidebar? If it does, select it and run First Aid - this checks and repairs the file system, which is the usual fix after an unclean shutdown caused by a power failure.
If the drive shows up in Disk Utility but doesn’t mount even after First Aid, please let us know what file system it’s formatted with (shown in Disk Utility when you select the drive). For example, if it’s NTFS, macOS can only read it with third-party software, and a file system check would need to be done on a Windows PC, as mjw suggested above.
Also, could you confirm what exactly is on this drive - your Roon database backups, your music files, or both? That will help us guide you on the recovery path once the drive is readable again.