1. I note your proposed save path starts with
/Volumes... you need to be very sure you have that filepath correct, and that you do not have duplicate mount points for that given volume (this does happen in Mac OS sometimes) which you need to check in Terminal by traversing to that directory and listing all mounted volumes - if there are duplicates, you'll see them, and if there are, that will be a question best posted to https://apple.stackexchange.com/questions not GD.SE.
2. I also note that the name of the Volume to which you wish you write your save for web files is Backup... if indeed that is an identified Time Machine Backup volume, the directories may well be permissions-protected, correctly preventing Photoshop from writing there, and you may be able to write to that location by drag n drop for the default only because you're operating from an improperly-elevated user account; I would establish a target area for these files which is not in a Backup volume.
Bear in mind that if indeed that volume is in use for backups, and you are writing changes to that volume, a) those files are not themselves backed up and b) sheer luck is all that's kept you from a corrupted backup.
3. This issue is in fact squarely out-of-scope as tech support - see https://graphicdesign.stackexchange.com/help/on-topic for details.
Hope this helps.