Do belts on belt-drive bicycles stretch under load and spring back? Reputedly they don't stretch over their lifetime
Everything stretches under load.  How much is the question.

The belt manufacturers should have technical data, including stress/strain graphs, modulus numbers, or other "hard" numbers.

But, generally speaking, carbon fiber and steel both have a modulus of around 200.  It's not clear now much carbon fiber is in the belts (and the cross-section area times the modulus effectively tells you how much stretch will occur), but when you consider the thinnest parts of a steel chain, and the fact that the pins will tend to flex in tension, it's probably comparable.

In any event, stretching should not be a concern so long as it's not sufficient to cause the belt to skip on the cog, or some other mechanical issue.