ci: add integration check for cartridge module

This patch extends the 'integration.yml' workflow and adds a new
workflow call for running tests to verify integration between tarantool
and the cartridge module.

Part of #5265
Part of #6056
Closes #6512

.github/workflows/integration.yml

@@ -22,3 +22,9 @@ jobs:
     uses: tarantool/vshard/.github/workflows/reusable_testing.yml@master
     with:
       artifact_name: tarantool-ubuntu-focal-${{ github.sha }}
+
+  cartridge:
+    needs: tarantool
+    uses: tarantool/cartridge/.github/workflows/reusable-backend-test.yml@master
+    with:
+      artifact_name: tarantool-ubuntu-focal-${{ github.sha }}