Speaking as a former (quite a few years now) insurance adjuster, they have an obligation to the value of the vehicle at the time of the loss, rather than to put you into a new vehicle. That being said, there are some protections to give you a good value, although as all insurance, it values dramatically by state law and insurance company.
For the California total loss claims I handled, the company had to provide comps - same/similar year, make and model in a localized geographic region in the recent (6 months or so) past to fully establish the value of the car. And the Total loss team would haggle a bit if you had factual evidence that supported an increased value (for example, I got a request for increase accompanied by a 2 week old receipt for 4 brand new tires, which did indeed bump the claim up $120 or so).
So if the final payment doesn’t include something similar, to make sure you’re getting current value rather than pre-shortage value, I’m sure you could ask for the like or other verification of value independent of their mere say-so. But it’s almost certainly not going to put you in a a brand new car. Under normal circumstances, I would also suggest (if you had a spare vehicle) waiting until year-end sales to get a last year model that hadn’t sold yet… but this is the time we live in.
Depending on your vehicle though, the settlement might put you at a place where you could get a brand new but smaller / less featured vehicle, although I doubt this is an option you have or want or you’d have mentioned it earlier.
Lastly, as mentioned upthread, if you know a good mechanic or friend who works on the cheap and want to take the risks, take the Total loss, minus the salvage value, get a salvage title on the vehicle, and fix it to the best of the mechanics ability, possibly with quality salvage or non-OEM parts. But that’s another kettle of fish.
PS - when working the claim, check with both your carrier and the alt carrier as to who can do the best job for a rental during the settlement / replacement phase. With current rental costs, your own carrier may or may not have sufficient to get you a car, and it generally caps at 30 days, which may not be enough to find something. The responsible party may go longer, but in most cases both will cut off rental reimbursement shortly (3-7 days) after a settlement is made, and you’re on the hook past that even if you still haven’t found a car. And at $60-100 a day for a rental, you want that spelled out before it’s out of pocket.