What happens if the insurance company "totals" the car, but you want to keep it?

Why guess, here is the official word from the state-

https://www.nh.gov/safety/divisions/dmv/title/salvage.htm

Thanks to all for the insights.

I talked to the NH DMV today as well as the Insurance company.
The insurance company will discuss the details (settlement, buying it back, etc) after their final in person assessment.

I had a similar experience. I’m curious about the taxes. What was taxed?

You’d need to talk to the tax officials in your own state. States all vary in this area.

They included the state sales tax I would pay on the replacement vehicle, assuming I would spend all of the money they paid for the replacement. Iirc, something around 5.8%.