The Netlify engineering team has migrated their Cypress tests from a GitHub action to a custom Netlify Build Plugin. This migration was done due to issues with the original workflow, such as failed tests on deploy previews and missing notification of test failures in production. The new plugin provides more control over testing and output, including running tests on deploy successes, updating status checks on GitHub, displaying information in the deploy summary, and posting Slack messages when tests fail in production. The team has built their own plugin to combine both Cypress and Percy visual regression tests, allowing for more flexibility in test execution.