How critical is it to have a perfectly level trailer?

Yes, the question is about towing level, not parking on the spot.
Towing level means more to the tow vehicle than to the trailer
Though ideally both are level
This means the frame of the Truck is parallel to the ground
AND the frame of the trailer as well.

This may require a rise or drop adapter on the hitch. But in this case level = Best control when stopping.