A coverage investigation means they have reason to believe the person did not have valid coverage at the time of the accident. This could mean there was a lapse in coverage on the policy, or maybe the car wasn't listed on the policy, or it was an excluded driver, or something else. It does not mean it definitely isn't covered, but it means there's a decent chance the person who hit you didn't have valid insurance at the time of the accident. I have seen this when someone made a payment on the last day to avoid cancelation, they just waited until the payment cleared and then paid the claim. I have also seen it where it was decided there was no coverage.

You have a few options. First you could go through your own insurance, but with small damage and high deductibles that probably won't get you too far ahead. But your insurance would subrogate, meaning that would try to collect from the person who hit you or their insurance (if it turns out to be valid). and if they collect, you get your deductible refunded. Subrogation takes a very long time usually, like 6+ months. You could also skip insurance and go straight to small claims court, but winning in court is easy and collecting is difficult. Or you can wait until the coverage investigation is concluded, and decide at that point.