[CI] Update to also format

.gitea/workflows/update-docs.yml

@@ -0,0 +1,35 @@
+name: Update docs
+on:
+  push:
+    paths:
+      - 'docs/**'
+jobs:
+  build_docs:
+    runs_on: ubuntu-latest
+    steps:
+      - name: Set up Git repository
+        uses: actions/checkout@v6
+      - name: Sign into gitea registry
+        uses: https://github.com/docker/login-action@v3
+        with:
+          username: ${{ vars.REGISTRY_USER_USERNAME }}
+          password: ${{ secrets.REGISTRY_USER_PASSWORD }}
+          registry: ${{ vars.REGISTRY_BASE_URL }}
+      - name: Run format of docs
+        uses: actions/latex-format@main
+        with:
+          workdir: docs
+      - name: Run build
+        uses: actions/latex-full@main
+        with:
+          workdir: docs
+          include_helpers: true
+      - name: Upload compiled docs
+        uses: actions/git-auto-commit-action@v7
+        with:
+          commit_message: "[skip ci] Build docs on push"
+          file_pattern: '*.pdf'
+          commit_user_name: LaTeX compiler [bot]
+          commit_user_email: actions@janishutz.com
+          commit_author: LaTeX compiler [bot] <actions@janishutz.com>
+          push_options: "--force"