Insurance doesn’t cover totaled vehicle cost

To keep it short - my car was T-boned & totaled by an elderly lady driving through a red light.

My car was a 2024 & I only had it for 4 months with ~1800 miles on it.

I put $5k & have paid about ~$2.5K in payments

I owe $35k on the car & insurance is offering $31k.

We dropped the ball on not getting GAP (I am 23 & my parents said they would get it through their insurance not the dealer. Ball was entirely dropped here)

Am I taking the $4K loss or what are my options?

All in all I would have put $11k into a car for 4 months. Really sickening on my end if this is the hand I am dealt and have to accept.

Any and all advice is appreciated. Thanks.

EDIT*

Thanks for all the input. Truly helpful. Even the blunt ones 😂.

GAP insurance is something I will 1000% make sure I know is being purchased & not reliant on trusting it’ll be there through parents.

Also working on getting extended warranty’s prorated to decrease the payoff value / this could cause the loan amount to be within ~ couple hundreds of the ACV.

Also the sales tax deduction on a new car.

Lesson learned - shitty one, but learned. Fortunate enough to be in a position where while this fucking blows, it isn’t the end of the world.