feat(auth): Enable resumable SignIn

[joon-won]

Description of changes

• Enable v6 users to have an option to continue SignIn process after a full browser reload by storing, then utilizing session in session storage

Issue #, if available

• Ability to resume authentication flow #10469
• Ability to resume authentication flow (v6) #12810

Description of how you validated changes

• Unit Tests added
• E2E for Custom Auth flow and SMS MFA added
• Manual testing

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]

⚠️ 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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