in every case I know of moving to qt greatly increased the quality of the ui. Though touchscreens in a car still suck everywhere.

cheap electronics will stand up to use in a car for years - something the fastest computers often fail at. I'm under NDA so I can't give more details.

Those cheap often boot instantly while more powerful ones often need a minute by the time everything is initialized.

I had presumed that car GUI/Infotainment systems were just in sleep or hibernated when the car is off, to shorten the startup time when switched back on.

Some part of it, yes. In the systems I worked on you had the "AC" - Automotive controller that was in a sort of deep sleep. But the "CG" - graphics controller was completely shut down.

They need to boot fast after the battery is replaced. Sleep also needs to not drain the battery. sometimes they will do a full shutdown after a week if sleep can still use power

So? Tesla can do it and they use the same thing like everybody else. Their UI feels apple like and yet they just use QT like everybody else.

The infotainment is just a small part of a car. It's the thing you interact with, sure but it's just the tip of the iceberg.