Ouch. Probably cheapest to get a new door and have it painted - repair would be a lot of work. I'd suggest go find a Tesla-approved bodyshop and ask for a price, and get quotes from a couple of other places. I'd guess it will cost $3-5000 in parts and labour, especially if the wheel arch needs work too (that might compound/polish out with a bit of touch-up, hard to tell with photos). If you can find a scrap yard white door that matches (they will exist - so many white Teslas!), it could be a lot cheaper - all depends how much leg work you want to put in.
Your call on insurance - having a claim WILL increase your premiums and you'll need to declare it when getting a quote with any other company, which will then increase the price - basically you will end up paying back in premiums a good portion of what you got for the claim. Unless it's astronomically expensive to fix, I'd just pay for it myself - expensive lesson learned.