docs(book): Add publish job (#890)

Signed-off-by: Nico Wagner <[email protected]>

.github/workflows/rust.yml

@@ -147,8 +147,12 @@ jobs:
         command: check ${{ matrix.checks }}
         rust-version: stable
 
-  ci:
+  publish:
+    if: ${{ github.ref == 'refs/heads/main' }}
     runs-on: ubuntu-latest
+    permissions:
+      contents: write
+      pages: write
     needs:
       - clippy
       - deny
@@ -159,5 +163,22 @@ jobs:
       - rustfmt
       - test
       - udeps
+    steps:
+      - uses: actions/checkout@v4
+      - uses: quarto-dev/quarto-actions/setup@v2
+        env:
+          GH_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+        with:
+          tinytex: true
+      - uses: quarto-dev/quarto-actions/publish@v2
+        with:
+          target: gh-pages
+          path: docs/book
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+
+  ci:
+    runs-on: ubuntu-latest
+    needs: publish
     steps:
       - run: exit 0