Migrate e2e from cypress tests to playwright

Cypress is blocked internally so I am struggling to run the e2e tests when pushing changes.

Playwright is the approved way to run these tests.

Start by locating the existing Cypress end-to-end tests and any Playwright setup in the repository, then check how the tests are run in CI. The migration is complete when the end-to-end coverage runs with Playwright instead of Cypress and can be executed without the internal Cypress restriction.

Written by the indexing model from the issue text.