Improve GitHub release workflow

This changes the existing script to just generate the release notes and delegate the actual publishing to the `softprops/action-gh-release@v1` action.

This allows us to delete the custom code, which failed recently in https://github.com/pytest-dev/pytest/actions/runs/7370258570/job/20056477756.

.github/workflows/deploy.yml

@@ -82,9 +82,14 @@ jobs:
         python -m pip install --upgrade pip
         pip install --upgrade tox
 
-    - name: Publish GitHub release notes
-      env:
-        GH_RELEASE_NOTES_TOKEN: ${{ github.token }}
+    - name: Generate release notes
       run: |
         sudo apt-get install pandoc
-        tox -e publish-gh-release-notes
+        tox -e generate-gh-release-notes -- ${{ github.event.inputs.version }} scripts/latest-release-notes.md
+
+    - name: Publish GitHub Release
+      uses: softprops/action-gh-release@v1
+      with:
+        body_path: scripts/latest-release-notes.md
+        files: dist/*
+        tag_name: ${{ github.event.inputs.version }}