PYTHON-5017 Use a separate PyPI publish step (mongodb#2042)

Author: blink1073

.github/workflows/release-python.yml

@@ -67,6 +67,23 @@ jobs:
 
   publish:
     needs: [build-dist, static-scan]
+    name: Upload release to PyPI
+    runs-on: ubuntu-latest
+    environment: release
+    permissions:
+      id-token: write
+    steps:
+      - name: Download all the dists
+        uses: actions/download-artifact@v4
+        with:
+          name: all-dist-${{ github.run_id }}
+          path: dist/
+      - name: Publish package distributions to PyPI
+        if: startsWith(inputs.dry_run, 'false')
+        uses: pypa/gh-action-pypi-publish@release/v1
+
+  post-publish:
+    needs: [publish]
     runs-on: ubuntu-latest
     environment: release
     permissions: