They will most likely pay the difference. It a shitty thing but it happens.
Wait for them to come back with the approval. They always try and give you a low ball offer first.
The only thing I would recommend is to make sure to have OEM parts only.
My last ///M got into an accident at a construction site. The construction company took blame for it. there insurance adjuster wrote me a check for $2k
which I refused to take. Took it to BMW and ask for the OEM AC Schnitzer parts and the bill came out to $16k. So they totalled her.
She is now the reason why I have a new car.
. She will be missed.