Look down on the circumstances from 1,000 feet. The insurance folks aren’t concerned with which of you was at fault. Each insurer will settle their own client’s claim.
To pursue an action against the other driver – you’d need to show he was at fault. And he’s in the same position to pursue an action against you. An offence such as `careless’ or `reckless’ driving would be strong supportive evidence. But then you (or he) would only recover what was lost outside of the insurer’s settlement.