Use build-and-inspect-python-package action (#10722)

This uses https://github.com/hynek/build-and-inspect-python-package to ensure our package is correct, both during testing and deploy,

.github/workflows/deploy.yml

@@ -28,25 +28,30 @@ jobs:
         fetch-depth: 0
         persist-credentials: false
 
-    - name: Set up Python
-      uses: actions/setup-python@v4
+    - name: Build and Check Package
+      uses: hynek/build-and-inspect-python-package@v1.5
+
+    - name: Download Package
+      uses: actions/download-artifact@v3
       with:
-        python-version: "3.7"
-
-    - name: Install dependencies
-      run: |
-        python -m pip install --upgrade pip
-        pip install --upgrade build tox
-
-    - name: Build package
-      run: |
-        python -m build
+        name: Packages
+        path: dist
 
     - name: Publish package to PyPI
       uses: pypa/gh-action-pypi-publish@release/v1
       with:
         password: ${{ secrets.pypi_token }}
 
+    - name: Set up Python
+      uses: actions/setup-python@v4
+      with:
+        python-version: "3.7"
+
+    - name: Install tox
+      run: |
+        python -m pip install --upgrade pip
+        pip install --upgrade tox
+
     - name: Publish GitHub release notes
       env:
         GH_RELEASE_NOTES_TOKEN: ${{ github.token }}