ci: Try to build examples in CI (open-telemetry#2711)

Co-authored-by: Harold Dost <[email protected]>

Author: cijothomas

.github/workflows/ci.yml

@@ -213,6 +213,24 @@ jobs:
           CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}
         with:
           fail_ci_if_error: true
+  build-examples:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toolchain@stable
+        with:
+          components: rustfmt
+      - uses: arduino/setup-protoc@v3
+        with:
+          repo-token: ${{ secrets.GITHUB_TOKEN }}
+      - name: Build examples
+        run: |
+          for example in examples/*; do
+            if [ -d "$example" ]; then
+              echo "Building $example"
+              cargo build
+            fi
+          done
   cargo-machete:
     continue-on-error: true
     runs-on: ubuntu-latest
@@ -232,4 +250,4 @@ jobs:
         with:
           tool: cargo-machete
       - name: cargo machete
-        run: cargo machete
+        run: cargo machete