The car is - and always is - your vehicle. As you are not going through your own insurer, you are not in any contract with the at fault insurer, so make sure you keep control over your asset. You will still be insured with your own insurer and it will not affect it the next year.
This is as long as you have gone through the third party insurer and not your own. It can get a little bit more complicated going through your own insurer in this type of situation which is why I always advise against it unless you really need too.

Ask the at fault insurer for a copy of their Engineers report for your vehicle, or a "full engineers version" of their "audatex assessment". For your car to be beyond economic repair, the repair cost need to be more than the value of the car. If they are not,your car is "NOT" a total loss, in this situation , request a cash in lieu settlement at the full cost of repair.