The main thing is to get the video recording from the parking management and go to the police with it right away. Make sure to file a hit-and-run report, even if the cars aren't next to each other anymore. Using the license plate from the video, the police will be able to identify the owner and driver, and then they'll deal with their insurance. You don't need to track down the person yourself - that's the authorities' job - just give them the evidence.
As for the parking management claiming you need to find the driver yourself - that's them trying to dodge responsibility. By law they have to provide the video recording when there's been a hit-and-run, and they have no right to refuse. If they start giving you a hard time, mention that you'll file a complaint about them refusing to hand over recordings during a hit-and-run investigation. Usually that does the trick 😊
After you go to the police, your insurance company can then work with the information from law enforcement. If your insurance keeps demanding that you find the driver yourself, file complaints against them with the RAS (Russian Union of Auto Insurers) - it's their responsibility to help identify the at-fault party when evidence exists, not to shift it onto the victim.