Duplicate the job that builds the docs across workflows

.github/workflows/build_documentation.yml

@@ -1,8 +1,6 @@
 name: Build the documentation
 
 on:
-  push:
-    branches: [main]
   pull_request:
     branches: [main]
 

.github/workflows/publish_documentation.yml

@@ -1,23 +1,25 @@
 name: Publish the documentation
 
 on:
-  workflow_run:
-    workflows: [Build the documentation]
-    types: [completed]
+  push:
     branches: [main]
 
 jobs:
   publish:
     name: Publish
     runs-on: ubuntu-latest
-    if: ${{ github.event.workflow_run.conclusion == 'success' }}
     steps:
       - name: Checkout the branch
         uses: actions/[email protected]
         with:
           persist-credentials: false
 
-      - name: Build docs
+      - name: Set up Python 3.9
+        uses: actions/setup-python@v1
+        with:
+          python-version: 3.9
+
+      - name: Build the documentation with Sphinx
         run: |
           pip install -r requirements-doc.txt
           sphinx-build -b html docs docs/build/html