Hello, I’ve been in food businesses for decades, I believe the cafe owner is responsible and should have a pest control program for his business to control the issue and rubbish stored in bins with lids closed. If you know someone reputable in the food industry ask them to take a peek at how clean or well maintained the restaurtant and back/rubbish area is, although you’ve already said its unclean generally.
I agree with talking with the restaurant owner but if they’re really negligent or not caring about the issue then the best option could be a call to the NSW Food Authority. They will send someone out to check the hygiene practises and unless grossly negligent, the restaurant owner will usually be given a warning and notice of what to do to rectify the problem within a period of time, they will be billed for the inspection. If the restauranter then fails to correct a problem found then penalty notices, fines start.
While you have the problem with your car the NSWFA will be concerned about public health and food safety especially if there’s an infestation of rats near food areas. You should also be able to talk to NSWFA about the problem without making a complaint to get their view on it.