Description of your changes

As described in the linked issue, some recent changes made to the way the packages were built broke the workflow that runs the integration tests. This PR applies the same changes by using the shared GitHub Action that is tasked with restoring the dependencies from cache & building the project.

Related issues, RFCs

Issue number: #1516

Checklist

• My changes meet the tenets criteria
• I have performed a self-review of my own code
• I have commented my code where necessary, particularly in areas that should be flagged with a TODO, or 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 change is effective and works
• The PR title follows the conventional commit semantics

Breaking change checklist

Is it a breaking change?: NO

• I have documented the migration process
• I have added, implemented necessary warnings (if it can live side by side)

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