How does car insurance work for 2 fully autonomous self-driving cars (no pedals, no steering wheel) that crash and both people broken bones?

As always the human that the vehicle is registered to is 100% responsible for any and all damages it causes.

Probably "no fault" insurance.  Your insurance covers you and your stuff and you have no liability for others, ie. damages, liability.  It can be made into law.  However, the next step is non-ownership of your car.  You will simply request one.   There will probably be "public" like self driving taxis, or groups, such extended families, organizations.  However/whoever you would find sharing a vehicle with to be acceptable.  So, you will have a personal umbrella insurance for yourself and share the cost of insurance in the pool of cars you use.  Part of the fee for using the car.

They are fully insured for millions of dollars for repair or replacement costs [others are self-insured]. Premium is usually $10,000 per month for each. By the time everyone starts using it, premium will be same as it is today for ordinary cars. The government may initially subsidize the costs.