[BUGFIX] Enable ProcessedFiles to do file exists

Make storage 0 folder readable, browsable and writable
to mitigate the problems that arise with non
readable processing directories.

Also allow file exists in general if the
identifier in subject is in processing folder.

Resolves: #51808
Releases: 6.0, 6.1, 6.2
Change-Id: I1959d7911d955592db1771d608e8fafcc26c45e9
Reviewed-on: https://review.typo3.org/23660
Reviewed-by: Horst-Dietrich Frank
Tested-by: Horst-Dietrich Frank
Reviewed-by: Anja Leichsenring
Tested-by: Anja Leichsenring
Reviewed-by: Jakob Hombsch
Tested-by: Jakob Hombsch
Reviewed-by: Wouter Wolters
Tested-by: Wouter Wolters