Dakota, I owe you an apology. I thought I had responded to your original question & just realized I hadn’t.
Interesting, our pets never seemed to suffer from separation anxiety when another pet had to spend time at the vet. We did however have some major grieving after the loss of another furry family member. The level of grieving, or lack of grieving, depended on how attached they were to each other.
I agree with the suggestions, extra attention, plenty of exercise including long walks, new toys, love and time. Not just walking in the usual locations, try going to fun new places for a distraction. I would be very hesitant to use medications, only as a last resort.