I wish I had some tried-and-true advice for you, but I don't. Danny grieved the loss of his best buddy Charlie the cat for six months. We couldn't use Charlie's name or the word "cat" without Dan racing around the house, whimpering, looking for his friend. I think it probably helped that we also had Sunnie in the house, but I wouldn't swear to that.
They shared beds and Charlie's toys never got left out (fur, feathers), so there was nothing to make a decision about with regard to keep/hide.
I discouraged abject neediness, crawling into my lap, that sort of thing....and I used "it'll be OK" a lot. I think it was all just a matter of time, though.
Dan's anxiety seemed to grow out of this but it's obvious that he inherited it from his mother so I think the timing may have just been coincidental.
In hindsight, I wish I had tried something to lessen anxiety with Dan. Two of the things I've subsequently started using with both Sunnie and Danny are calming collars and a homeopathic calming product. The homeopathic product really brought Sunnie's anxiety down a lot (did NOT eliminate it) and kept Dan a good bit more mellow. The calming collars are mostly for thunder, fireworks, and high wind...but would be good for separation anxiety, etc., too.
https://www.calmingcollars.com/
https://www.nativeremedies.com/petal...-granules.html