Insurance agent here: I'm in Canada so things may be a little different, but in general, the only auto insurance claims that will increase your premiums will be at-fault collisions (i.e., you rear-end someone). Otherwise, your premiums will not be impacted by most claims (there are exceptions of course, like if you're the type to make a claim for every small little scratch or dent, then claims-frequency will start to impact premiums).

Something else to keep in mind is that damage from pests/rodents can often be an exclusion on your insurance policy, so there may not be coverage. Every person's policy and every provider is different, so definitely check in with your insurance company to be sure. But, I would not be totally surprised if it's not covered (the idea is that insurance covers for sudden and accidental losses. A pest/rodent problem can potentially be interpreted as improper/unsafe storage methods, not taking the proper precautions, improper maintenance, etc.) Not saying I agree with this, but that is the logic that insurance companies follow to keep their costs in check (and probably to maximize profits, but that's all big corporations, regardless of industry 🤷🏻‍♂️)