There are already quite a few integration tests, and they are a great success, they reliably uncover issues that we also face with the actual zombienet so far. Hence, we should integrate as many as possible, and I saw that the runtimes repository has recently enhanced their integration test suite: https://github.com/polkadot-fellows/runtimes/tree/main/integration-tests/emulated/tests/assets/asset-hub-kusama/src/tests
Porting upstream integration tests has proven to be fairly straight forward, so we should definitely do that.