Automatic merge from submit-queue

Add test for provisioning with storage class

This PR re-introduces e2e test for dynamic provisioning with storage classes.

It adds the same test as it was merged in PR #32485 with an extra patch adding region to AWS calls. It works well on my AWS setup, however I'm using shared company account and I can't run kube-up.sh and run the tests in the "official" way.

@zmerlynn, can you please try to run tests that led to #34961?

@justinsb, you're my AWS guru, would there be a way how to introduce fully initialized AWS cloud provider into e2e test framework? It would simplify everything. GCE has it there, but it's easier to initialize, I guess. See https://github.com/kubernetes/kubernetes/blob/master/test/e2e/pd.go#L486 for example - IMO tests should not talk to AWS directly.