This is a fun idea!
There is a lot of information and not a lot of explanation which makes it difficult to understand what is expected from us. I ended up parking cars by following instruction and did not use 90% of the UI.
The concept is cool, but the gameplay is quite heavy. I guess I faced a few bugs, like the initial position of a car being perpendicular to the entrance, which is annoying. And the gameplay feels very heavy and slow. In order to increase challenge without overloading with moving parts and all you could tweak the driving mechanic to be faster and more slopy and engaging, making it harder to drive it correctly, break consistently, etc, with some crash noises when you hit another car. I can see this as a very fun party game.
Music is cool!
As others have mentioned, I don't see how it is related to the theme at all (maybe trough the synthwave music but it is not mentioned anywhere ^^)