[3.13] gh-136155: Docs: check for EPUB fatal errors in CI (GH-134074) (#137538)

Co-authored-by: Maciej Olko <maciej.olko@affirm.com>
Co-authored-by: blurb-it[bot] <43283697+blurb-it[bot]@users.noreply.github.com>
Co-authored-by: Adam Turner <9087854+AA-Turner@users.noreply.github.com>

.github/workflows/reusable-docs.yml

@@ -66,7 +66,7 @@ jobs:
       run: |
         set -Eeuo pipefail
         # Build docs with the nit-picky option; write warnings to file
-        make -C Doc/ PYTHON=../python SPHINXOPTS="--quiet --nitpicky --fail-on-warning --warning-file sphinx-warnings.txt" html
+        make -C Doc/ PYTHON=../python SPHINXOPTS="--quiet --nitpicky --warning-file sphinx-warnings.txt" html
     - name: 'Check warnings'
       if: github.event_name == 'pull_request'
       run: |
@@ -102,3 +102,30 @@ jobs:
     # Use "xvfb-run" since some doctest tests open GUI windows
     - name: 'Run documentation doctest'
       run: xvfb-run make -C Doc/ PYTHON=../python SPHINXERRORHANDLING="--fail-on-warning" doctest
+
+  check-epub:
+    name: 'Check EPUB'
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+    steps:
+    - uses: actions/checkout@v4
+      with:
+        persist-credentials: false
+    - name: 'Set up Python'
+      uses: actions/setup-python@v5
+      with:
+        python-version: '3'
+        cache: 'pip'
+        cache-dependency-path: 'Doc/requirements.txt'
+    - name: 'Install build dependencies'
+      run: |
+        make -C Doc/ venv
+        python -m pip install epubcheck
+    - name: 'Build EPUB documentation'
+      run: make -C Doc/ PYTHON=../python epub
+    - name: 'Run epubcheck'
+      continue-on-error: true
+      run: epubcheck Doc/build/epub/Python.epub &> Doc/epubcheck.txt
+    - run: cat Doc/epubcheck.txt
+    - name: 'Check for fatal errors in EPUB'
+      run: python Doc/tools/check-epub.py