With SA you need a softly softly approach. Also, it may not actually be full blown SA, but just a settling in thing. This often happens with rescues in a new home as it is very disruptive for them
It may just be a time thing. Friends of ours have gone through this recently.
Try building up the time you leave Parsley for, starting with just going outside the front door and waiting quietly for a few seconds before coming back in. Then build it up by tiny increments until ten minutes, 20, 30 etc.
Dogs are all different, some benefit from a leaving routine, others feed off this in their anxiety (ie when they see you pick up the keys or put their coat on the anxiety starts). You'll have to see in time what works. For us, Dylan hates being left (even though he has Clive) but benefits from being asked to go to bed. He knows he is being left, but this prepares him and works for him.
Leaving Parsley with a treat ball is a good idea - does he use it?
When you return try not to make a big fuss as with some dogs this makes the difference between you being there and not being there greater - ie no fun without you, fun with you.
Another thing is where he is left. Some dogs prefer being left in a crate, or a single room as too much space can make them anxious. Others (like my friend's dog) SA disappates is they are left to roam. Try different things to see if it helps.
Hope this gives you some stuff to work on. Best of luck, and hopefully it will just be a settling in issue rather than a bigger one.