Cypress has a few configuration options to specify custom folder structure.
For that you will need to have cypress.json file in the root of your project and specify the following structure there for cypress to properly pick up the files in test/cypress/:
{
"fixturesFolder": "test/cypress/fixtures",
"integrationFolder": "test/cypress/integration",
"pluginsFile": "test/cypress/plugins/index.js",
"screenshotsFolder": "test/cypress/screenshots",
"videosFolder": "test/cypress/videos",
"downloadsFolder": "test/cypress/downloads",
"supportFile": "test/cypress/support/index.js"
}
More info in the cypress docs.