AVRO-3868: [Rust][CI] Check consistency between the doc comment in li…

…b.rs and README.md (#2510)

* Cache cargo-rdme

* Unuse cargo-install

* Trigger GA to check effect of cache

.github/workflows/test-lang-rust-ci.yml

@@ -80,6 +80,22 @@ jobs:
           components: rustfmt
           targets: ${{ matrix.target }}
 
+      - name: Cache cargo-rdme
+        if: matrix.rust == 'stable' && matrix.target == 'x86_64-unknown-linux-gnu'
+        uses: actions/cache@v3
+        with:
+          path: ~/.cargo-${{ matrix.rust }}/cargo-rdme
+          key: cargo-rdme-
+
+      # Check if the doc cumment in avro/src/lib.rs and avro/README.md are in sync.
+      - name: Run cargo-rdme
+        # The result is environment independent so one test pattern is enough.
+        if: matrix.rust == 'stable' && matrix.target == 'x86_64-unknown-linux-gnu'
+        run: |
+          cargo install --root ~/.cargo-${{ matrix.rust }}/cargo-rdme --locked cargo-rdme
+          export PATH=$PATH:~/.cargo-${{ matrix.rust }}/cargo-rdme/bin
+          cargo rdme --check
+
       - name: Rust Format
         if: matrix.target != 'wasm32-unknown-unknown'
         run: cargo fmt --all -- --check