Description of your changes

During the last workflow refactoring we removed the API docs build step. Sadly, the docs publish workflow did not fail when trying to copy api folder that does not exist. I have added the build api docs step.

How to verify this change

Related issues, RFCs

Issue number: closes #1366

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
• I have made corresponding changes to the examples
• My changes generate no new warnings
• The code coverage hasn't decreased
• I have added tests that prove my change is effective and works
• New and existing unit tests pass locally and in Github Actions
• Any dependent changes have been merged and published
• 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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