PYTHON-4420 Fix GitHub Actions publish job (#1626)

Author: blink1073

.github/workflows/release-python.yml

@@ -136,7 +136,7 @@ jobs:
           find . -type d -empty -delete
       - uses: actions/upload-artifact@v4
         with:
-          name: all-dist-${{ github.job }}
+          name: all-dist-${{ github.run_id }}
           path: "./*"
 
   publish:
@@ -151,7 +151,7 @@ jobs:
     - name: Download all the dists
       uses: actions/download-artifact@v4
       with:
-        name: all-dist-${{ github.job }}
+        name: all-dist-${{ github.run_id }}
         path: dist/
     - name: Publish distribution 📦 to PyPI
       uses: pypa/gh-action-pypi-publish@release/v1