My Arlo whom we adopted at 2 had terrible anxiety when we left him at home even just for an hour or so. When we returned we found that he had been running through the house "throwing things." He damaged some things that I valued but we were able to deal with it. Here is what worked for us.
I had a "talk" with him just before we left him alone. This may sound weird to some, but I told him that we would be back, petted him, told him he needed to take care of things while we were gone and gave him a treat. He watched me with his big eyes, got very calm and quiet, and didn't try to beat us out of the door when I did this. In a fairly short time he understood that we would always come back to him and the tearing up the house stopped.
I still do this if I spot him getting anxious if we are about to leave and it seems he understands. As many of you will remember, we found that he had been shot with birdshot before we adopted him (We still get angry thinking about it.) so he had reason to be fearful.
This worked for us, but no matter what you try remember that it will not be resolved immediately so be patient.
And good luck!