I think there is almost ZERO chance that this OP would "save money" by paying for the repair themselves, even if insurance rates goes up. Said another way, even if insurance rates go up, they normally go up for "an amount" for 3 years. Lets say this OPs insurance rate goes up 1k a year for three years. In order for the OP to "save money" by paying out of pocket instead, the repair would have to cost 3k or less.
I doubt OPs insurance rate would go up 1k a year, and I SERIOUSLY doubt that repair is less than 3-4k, done by a reputable body shop, that is equipped / certified to work on teslas. Of course, OP might be able to find a shop to do it for less, but I have no idea why anyone with insurance would do that for something like this.
Say insurance rates go up 500 a year, thats $1500 over the three years that increase would happen. How many are looking at those pictures and seeing $1500 or less in damage?
Translation: i agree with
@dmurphy , which is absolutely no surprise, that the OP should just file with insurance (which it sounds like they have done), and move forward, and not worry too much about if or whatever the insurance increase might be, because its very unlikely that its more than the cost of the repair.