We jump ahead 4 major versions with this upgrade, which brings these
changes:

- The default location of test files is now `cypress/e2e` instead of
  `cypress/integration`, and our test files have moved accordingly.
- The default spec file suffix has changed to `.cy.js`, and our test
  files have been renamed accordingly.
- The configuration file is now called `cypress.config.js` instead of
  `cypress.json`, and has a slightly different structure.

See https://docs.cypress.io/guides/references/migration-guide for more
details about these changes.

Finally, a dummy/no-op plugin was removed.