The good news first. You should be able to commit/delete the snapshots without issues.
Let me explain:
The reason you see same location for the vmdk's in the VM's settings is because all snapshots are located in the VM's "home" folder on the sata datastore. The base vmdk's of the disks however are located on the other two datastores. The base disks are definitely thin provisioned and I can't tell you why it shows thick!?
Snapshot "yyyz-file-1-000002.vmdk" (~192 GB) belongs to the virtual disk the apps datastore witch has ~1.1 TB free disk space, so no issue with this one. The other two snapshots "yyyz-file-1-000001.vmdk" (~2 GB) and "yyyz-file-1_1-000001.vmdk" (~363 GB) have their base disks on the filer datastore, which currently has ~440 GB free disk space. Unless I'm mistaken and according to the screen shots, you have enough free disk space on the apps and filer datastores to safely commit/delete the snapshots. Just make absolutely sure the backup application (Veeam) does not run during this time and tries to create another snapshot!
André