My insurance
They are considering me as at fault
You are not obligated to accept their offer, you can definitely negotiate with them.
A relative recently go a really low offer from insurance, at first they were willing to gove him and extra few hundred, but after agruing and asking to deal with someone else, they offered an additional $2k(+tax) to settle. At this point it's still a low offer, so he may get a private adjuster to fight for another few $k.
I know someone who got another $7k with a private adjuster, but that was when the car market was much hotter.
All that being said, the car market has been cooling down, so it really makes sense that your car is worth less than it was a few months ago.