[Azure][Storage] Update Error response for accessing private container without access

[landscapepainter]

This updates the temporary solution implemented at #3791

Error was incorrectly handled when the user attempted to access a private container without access. This PR fixes with correct error response.

Tested (run the relevant ones):

• Code formatting: bash format.sh
• Any manual or new tests for this PR (please specify below)
  • Manually try to use private container without access as a source from task.yaml raises:

sky.exceptions.StorageBucketGetError: Failed to access existing bucket 'test'. This is likely because it is a private bucket you do not have access to.
To fix:
  1. If you are trying to create a new bucket: use a different name.
  2. If you are trying to connect to an existing bucket: make sure your cloud credentials have access to it.

• All smoke tests:
  • pytest tests/test_smoke.py::TestStorageWithCredentials --azure
• Relevant individual smoke tests: pytest tests/test_smoke.py::test_fill_in_the_name
• Backward compatibility tests: conda deactivate; bash -i tests/backward_compatibility_tests.sh

[landscapepainter]

@romilbhardwaj This is ready for a look!

[romilbhardwaj]

As discussed offline, we may want to retain some checks similar to this for the case where the storage account is accessible but some of the containers in the account are private.

[landscapepainter]

Thanks for catching this. Reverted the removal!

[landscapepainter]

@romilbhardwaj This is ready for another look!

[romilbhardwaj]

Thanks @landscapepainter! LGTM if tests pass.