chore(github): run update-book-cli in the lint workflow (#8335)

Signed-off-by: jsvisa <delweng@gmail.com>

.github/workflows/lint.yml

@@ -107,6 +107,25 @@ jobs:
           components: rustfmt
       - run: cargo fmt --all --check
 
+  book:
+    name: book
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toolchain@master
+        with:
+          toolchain: "1.76" # MSRV
+      - uses: Swatinem/rust-cache@v2
+        with:
+          cache-on-failure: true
+      - run: cargo build --bin reth --workspace --features ethereum
+        env:
+          RUSTFLAGS: -D warnings
+      - run: ./book/cli/update.sh target/debug/reth
+      - name: Check book changes
+        run: git diff --exit-code
+
   codespell:
     runs-on: ubuntu-latest
     timeout-minutes: 30
@@ -127,7 +146,7 @@ jobs:
     name: lint success
     runs-on: ubuntu-latest
     if: always()
-    needs: [clippy-binaries, clippy, crate-checks, docs, fmt, codespell, grafana]
+    needs: [clippy-binaries, clippy, crate-checks, docs, fmt, book, codespell, grafana]
     timeout-minutes: 30
     steps:
       - name: Decide whether the needed jobs succeeded or failed