test(e2e): add public verification flow tests (#349)

[daree-dev]

Closes #349

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Description

Please include a summary of the changes and related context.

Type of Change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Changes Made

Testing

Please describe the tests you ran and how to reproduce them:

• Unit tests pass
• Integration tests pass
• Manual testing completed

Test Coverage:

Checklist

• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests passed locally with my changes
• Any dependent changes have been merged and published
• If this PR adds a new directory or key file, I have updated docs/folder-structure.md.

Screenshots (if applicable)

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Additional Notes

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