Parachains can conveniently be tested locally with polkadot-launch to ensure a specific runtime release will produce blocks and perform e2e tests.
Is there an example of how to do these kinds of tests in github actions automatically?
polkadot-launch is being deprecated in favor of zombienet.
Also, check parachains-integration-tests. It is the tool Parity uses for Common Good Parachains. You can find the tests here: https://github.com/paritytech/cumulus/tree/master/parachains/integration-tests