Move integration tests into test/integ

[zastrowm]

Description

This unifies the package & integ tests under one directory, also co-located with test artifacts, resulting a cleaner directory structure.

Type of Change

Refactor

Testing

How have you tested the change?

• I ran npm run check

Checklist

• I have read the CONTRIBUTING document
• I have added any necessary tests that prove my fix is effective or my feature works
• I have updated the documentation accordingly
• I have added an appropriate example to the documentation to outline the feature, or no new docs are needed
• My changes generate no new warnings
• Any dependent changes have been merged and published

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