My grandmothers cat was attacked by a neighbor’s dog — what (if anything) can we do?

Sorry if it’s not the right sub to ask but wondering if anyone else has gone through something similar.

My grandmother has video footage of a dog running up on her porch and attacking her cat, resulting in several injuries to the cats underside which required surgery and he’s now staying at the vet for a second night tonight. We believe the dog belongs to someone nearby due to the dog having a collar on and appearing to be fairly healthy (I know this doesn’t necessarily mean anything but I’m hoping it’s not a stray). I called animal control and they advised us to make a report with BPD and in turn BPD would contact AC to come search for the dog. So far the vet bill has accumulated over $800 and is subject to additional charges as the night progresses. We intend to find the owner of the dog and go after them for vet bills but im hoping someone can provide me with some insight to what else (if anything) we could do to help this process or if it’s even worth it to try. FWIW this happened in Roebuck Springs.