This is an overview of how we got our e2e cypress tests running for our Laravel backend, and React frontend. Even if your stack is identical to ours, your environment may still slightly differ depending on versions, and providers.
API Docker Image - Laravel app TL;DR, Create a single Docker image for your Laravel App + webserver, and use it as a Gitlab https://docs.gitlab.com/ee/ci/services/ #motivation Motivation
registry.gitlab.com/your_project/api_ci:latest would be your API Laravel app, bundled in a single docker image with your web-server.