Port Cypress tests to Playwright

[tijlleenders]

Is your feature request related to a problem? Please describe.
It's very annoying when we have two frameworks for tests when we can have one.

Describe the solution you'd like
Port all the Cypress to Playwright and delete Cypress dependency.

Describe alternatives you've considered
None.

Additional context
None.

[tijlleenders]

@vinaybadgujar102 I think we don't have any more tests in Cypress, right?
Then we only need a PR to remove all Cypress mentions and dependencies to close this issue.

[vinaybadgujar102]

@tijlleenders Some tests are remaining. In #1929, only the failing test was migrated. Migrating all the tests in that PR would have made it unrelated and hard to review.