github: Get Trusted Publisher workflow working

[bkeryan]

Restructure Publish-Package.yml to use multiple jobs with the minimum permissions needed:

• Run checks by calling PR.yml (default read-only permissions)
• Build distribution package and upload as an artifact (default read-only permissions)
• Upload distribution packages to PyPI (full write permissions)
• Update package version for next time (needs contents:write and pull-request:write, also a PAT enables running checks on the newly created PR)

Tested by publishing https://github.com/bkeryan/python-styleguide/releases/tag/v0.5.0 to TestPyPI:

• TestPyPI: https://test.pypi.org/project/ni-python-styleguide2/#history
• Job log: https://github.com/bkeryan/python-styleguide/actions/runs/16176351138
• Update version PR: chore: Update project version - testpypi bkeryan/python-styleguide#2

[github-actions]

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