Mac OS 12.4 I could not recover purgeable space no matter what I did. I lost access to 660GB of HD space. Could not write to my HD. Spent 4 hours trying everything I could think of. Hint was it was a time machine problem. I had been trying to recover an Iphone backup, when all this started. So the problem was due to TimeMachine Local Snapshots being created and being reported as purgeable space. System would not delete them even when I turned of TimeMachine. Here is the trick. From the terminal.
tmutil listlocalsnapshotdates
You will get a list of dated snapshots. For example.
tmutil listlocalsnapshotdates 2022-06-22-162101 2022-06-22-172133 2022-06-22-182533 2022-06-22-192000
For each snapshot run tmutil deletelocalsnapshots Example tmutil deletelocalsnapshots 2022-06-22-162101
Problem solved!
Four fffing hours!