Make TestAzureDriverRetriesHandling tests more resilient

https://gitlab.com/gitlab-org/container-registry/-/jobs/9243222332

The tests rely on the fact that only the code injects the failures, and this is not the case in case when backend is also throttling requests.

In order to prevent false positives/negatives we need to check the responses we get from backend in the injector before we modify them. If they are not successful, we need to restart the test.