Add gitub workflow action to check docs

.github/workflows/rust.yml

@@ -136,9 +136,9 @@ jobs:
       - name: Verify Working Directory Clean
         run: git diff --exit-code
 
-  # Run doc tests
+  # Run `cargo test doc` (test documentation examples)
   linux-test-doc:
-    name: cargo doctest (amd64)
+    name: cargo test --doc (amd64)
     needs: [ linux-build-lib ]
     runs-on: ubuntu-latest
     container:
@@ -157,6 +157,25 @@ jobs:
       - name: Verify Working Directory Clean
         run: git diff --exit-code
 
+  # Run `cargo doc` to ensure
+  linux-rustdoc:
+    name: cargo --doc
+    needs: [ linux-build-lib ]
+    runs-on: ubuntu-latest
+    container:
+      image: amd64/rust
+    steps:
+      - uses: actions/checkout@v3
+      - name: Setup Rust toolchain
+        uses: ./.github/actions/setup-builder
+        with:
+          rust-version: stable
+      # Note: this does not include dictionary_expressions to reduce codegen
+      - name: Run cargo doc
+        run: |
+          export RUSTDOCFLAGS= "-D warnings -A rustdoc::private-intra-doc-links"
+          cargo doc --document-private-items --no-deps --workspace
+
   # verify that the benchmark queries return the correct results
   verify-benchmark-results:
     name: verify benchmark results (amd64)