A dog with severe anxiety won’t be distracted by even the tastiest treats. You’ll need to slowly get him used to your absence.
He may start to get nervous when he sees signs you’re about to leave, like putting on your shoes or picking up your keys. So do those things, but then don’t leave. Put on your shoes and then sit down at the table. Pick up your keys and watch TV. Do this over and over many times a day.
When your dog starts to feel less anxious about that, you can slowly start to disappear. First just go on the other side of the door. Ask your dog to stay, then close an inside door between you. Reappear after a few seconds. Slowly increase the amount of time you’re gone. Put on your shoes and pick up your keys. Ask your dog to stay while you go into another room.
As he gets more used to the “stay game,” increase the amount of time you’re gone. Then use an outside door, but not the same one you go out every day. Make sure your dog is relaxed before you leave.
Only you can tell if your dog is ready to be left alone for longer periods. Don’t rush things. Give him a stuffed treat when you’ve built up to 10 seconds or so apart. Always act calm when you leave and when you return.
Gradually build up the time until you can leave the house for a few minutes. Then stay away for longer and longer periods.