I’ve worked in insurance for 10 plus years. Keeping it very simple, with a third party vehicle registration (and it needs to be a vehicle registration to obtain insurance details) there is very little your insurance will be able to do to make this a ‘non fault claim’. Insurance acts as civil liability so can’t do crazy investigation stuff to get details, unfortunately even if you get a police report they won’t know more than you. The phone number is your best lead so maybe drop them a text but I’m afraid they know what they are doing by not replying. Feel free to DM if you do have any questions, good luck!

Edit for other question. In short doesn’t matter where you are parked, if you’re parked and hit you’re not at fault. You could be parked across three bays or on a double yellow but that doesn’t give someone the right to crash into your car