Add CI check that integration tests compile (#12090)

.github/workflows/_test.yml

@@ -44,6 +44,14 @@ jobs:
         shell: bash
         run: make test
 
+      - name: Install integration dependencies
+        shell: bash
+        run: poetry install --with=test_integration
+
+      - name: Check integration tests compile
+        shell: bash
+        run: poetry run pytest -m compile tests/integration_tests
+
       - name: Ensure the tests did not create any additional files
         shell: bash
         run: |