Hi ssd008.
The problem I believe is simply the fact that your drive was corrupted or physically damaged before we started.
The extent and type of that corruption or damage was impossible to say from our end, and it now transpires from your recovery attempts that your drive appears to have had some bad sectors.
Bad Sectors Explained:
How many bad sectors and whether they are physical damage or data corruption was again impossible to tell without having it sitting in front of us and carrying out various tests.
The $Badclus file, as Augeas alluded to above, is simply a meta file where the drive controller stores the location of all bad sectors on a drive, and prevents any further writing to those sectors.
Carrying out a Quick Format clears the stored data from the $Badclus file which means it no longer has any idea where the bad sectors are. I believe this is why it now shows as being the same size as the entire drive although it probably takes up very little space at all.
This information is a simplified version of my researching many many google hits on the $Badclus file. Not completely my own knowledge as it's a complex subject.
Just for info, the bad sectors could have caused a search for the lost partition to fail. Impossible to say for sure.
It was just just a windows quick format (as you requested). Not sure how to request windows to format ssd, I assumed it knows how to Quick format SSD.
Windows does know how to format an SSD, but I believe you have to select "Quick Format" somewhere during the initial set up of the format. Do you remember specifically doing that? I don't have an SSD to check this myself.
As to your data, I'm sure it will still be there as the $Badclus file doesn't overwrite the entire drive as it appears to show, but how to now get at that data I'm not sure.
Running "Chkdsk" may be an option as it may repair any soft bad sectors and mark any hard bad sectors so they won’t be used again.
How to Check a Disk from Windows: (CheckDisk in Win 7, 8 and 10)
I don't have any personal experience of using Chkdsk on a corrupt drive, so others contributing may help here. If successful a scan with Recuva could have better results.
Or, if your files are very important, it could be that the only course of action now is professional recovery, but even that may not be an option depending upon the physical state of your drive.