Most likely the hard drive in your Mini is failing which means it may be very difficult to recover any files from it. The first thing I would do if you don't have a backup is to run the Apple Diagnostics to see if any hardware issues are detected. Unfortunately the diagnostics don't detect many types of drive failures. If you have an external full macOS boot drive, then you can run DriveDx to check the health of the Mini's internal hard drive. If you don't have an external macOS boot drive, then I can provide instructions for creating and using a bootable Linux USB stick to check the health of the hard drive. Let me know if you are interested for the instructions.
I would not do anything else until you verify the health of the hard drive since the more the drive is accessed (or attempted to be accessed) or even powered on it will cause a drive failure to get worse where even an expensive data recover service will no longer be able to recover any files from the drive.
Be very careful how you proceed as you may only get one chance to recover the data on your hard drive so choose wisely.
FYI, you should always have frequent and regular backups.
