Migrate UI Cypress tests to Vitest Browser Tests

[Vladimir]

Clear and concise description of the problem

I wanted to remove Cypress for some time now because we have Playwright and the possibility to write component tests using Vitest Browser, and having a third package that can do the same seems bad.

Suggested solution

Migrate .cy.ts tests in package/ui to use Vitest Browser instead of Cypress.

Alternative

No response

Additional context

It's time to start actually dogfooding Vitest Browser.

Validations

• Follow our Code of Conduct
• Read the Contributing Guidelines.
• Read the docs.
• Check that there isn't already an issue that request the same feature to avoid creating a duplicate.