Reminds me of what I went through with Mattie. (Steve's cat)
I knew her since she was a kitten and after he passed, the family asked me to move in and take care of her while helping deal with the estate.
One year after his death, she started doing the same. Neighbor worked at the vet we used and knew us all. Got her in and found out she was in kidney failure and in discomfort, but pain would soon be coming. She didn't like the car rides (knew it was a vet ride), but after we got her up there, she just stayed in my arms until I set her on the table and then relaxed and nodded off. Angie and I pet her while talking to the doc, and then he gave her the shot and she went off to the rainbow bridge. We were bad for a couple of days, and then Angie got the call and set me up to get Kit and Micki the end of that week (when Angie had an aneurysm and died.
I guess it was meant to be because Kit very much was like Mattie (took a bit to get used to you but then loved you), while Micki was almost a clone of Angie's late cat, that passed before she started taking care of Steve and Mattie.
Now I wake up some nights when my pain medicine is do and reach over still thinking one of the cats is there until I wake up and realize I sent them back to their former owner. I've heard they adapted quickly to them and are doing well, but I do miss them. I've had some painful enough nights lately that if I knew everything was in order, I'd like that shot and welcome the chance to visit so many of the animals I knew/had access to growing up at the rainbow bridge.