Revert "fix(core): Check for storage initialization errors (#13938)"

[yuhengshs]

This reverts commit 0f5091780046b9556b98300c29fb970a0358bd70.

Temporarily revert this PR due logger error reported by our customer CoreStorageUtils - SessionStorage access failed: [Error: sessionStorage is not defined]

Description of changes

• revert the Added Session Storage and Default Storage try catch blocks

Issue #, if available

Description of how you validated changes

Checklist

• [ ] PR description included
• [ ] yarn test passes
• [ ] Unit Tests are changed or added
• [ ] Relevant documentation is changed or added (and PR referenced)

Checklist for repo maintainers

• [ ] Verify E2E tests for existing workflows are working as expected or add E2E tests for newly added workflows
• [ ] New source file paths included in this PR have been added to CODEOWNERS, if appropriate

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.

[github-actions[bot]]

⚠️ This PR includes changes to the "aws-amplify" package.json file, which can have library-wide implications.

Please ensure that this PR:

• Does not manually change "@aws-amplify/*" dependency versions, which may misalign core dependencies across the library

• Remove any export paths without a major version bump

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