The initial use of solar on the Prius was to power a ventilation fan while the car was parked, and the current version seems to specifically be designed to provide power to the air conditioner while driving. But, I also can't imagine the difference between cooling down the cabin is much different from parking in the sun or in the shade - you'd be running it continually to achieve "room temperature" during the entire drive either way.
You can't imagine that air conditioning power draw varies with the heat load that it is working against? As a heat-pump, it takes more energy to move more energy.
In the old days, they used duty cycle to adapt to the changing load. Modern ones do things like varying compressor displacement or compressor speed to adapt to the load. Variable frequency inverters are used to efficiently drive electric compressors.
The variable displacement trick is used in ones mechanically linked to internal combustion engines. It can vary the compression stroke to account for different load as well as different engine speed.
Watching power draw on my Leaf with LeafSpy, the AC seems to use between 500-1000W (maybe more sometimes, but that's just off the top of my head from a few times running it while driving).
At the low end maybe achievable with a full rooftop covered in solar panels, but probably not adequate at 1kW+.