My .02:
The standard process seems to be that the insurance company makes and initial "fair" offer, based on as little research and effort as possible (time is money), and hopes/expects that the customer will take it because some/many people aren't willing to make the small counter effort. Of course, there are also the people who will tell you your car is old and not worth much (and these people aren't always the ones working for the insurance company). The customer then either accepts the initial offer, or makes the small effort to counter the offer by doing a little research and talking to the adjuster or agent. This process either continues (effort and patience on behalf of the customer), or ends when the customer is happy with the offer- or determines the effort isn't "worth" it. No one else can tell you what that value is to you, nor should they try. For some people it's about a sense of fairness, for others money, and others like (or hate) the fight.
Personally, a little internet research from home and some phone calls/emails is easily worth it. As said, create a good list of TDI sales. Yes, the comps are often out of market, which is tough when CA prices are higher than elsewhere, but that's all you have to go on. Use all the internet engines and VW F/S sites to collect a dozen prior sales, followed by some F/S ads so the agent can see what it would cost to replace. Some engines allow you to search historical sales, which can also be super helpful.
I can't speak to "insurance companies" as a class, or generalize past this story to counter the inaccuracies stated in the posts above, but our friend's 2003 Jetta TDI 5M was hit at a stop light from behind, just prior to COVID. The car is perfect mechanically, but had 225,000mi and some exterior wear. The insurance company offered $2900. He eventually received just under $5000. Effort? Work? Just an internet search and some phone calls or emails. His comps included Jettas and Golfs, older TDIs (but not newer), and cars from all over the country.
No, they won't pay you for modifications, fancy stereo installs, or care about receipts for maintenance, but if you can make a good argument for market value, you'll typically see an appropriate response.
Oh, and he kept the car, we replaced the trunk and rear bumper cover, and it now has a happy 250,000 miles on it and is going strong.