From my own experience of escaped hamsters, the vets should not have given up on the escaped hamster after a few days.
Back in the 1970s when my children were young, we had a hamster who was a prize escapologist. Nothing we did could keep him in his cage.
He finally disappeared, and we resigned ourselves to his loss. However, a few weeks later I found a green tomato, which must have fallen down from the windowsill where it was put to ripen, pulled up against a hole at the bottom of a plate blocking the fireplace behind the gas fire.
We assumed the hamster was responsible, and put out some food for him overnight in case it was.
The food disappeared, so the next night, we put some food in the bottom of a plastic bucket, with a plank for a ramp. Sure enough, the next day, there was a forlorn looking hamster in the bottom of the bucket, none the worse for his adventure.
So, a message to the vets, don’t give up too soon.