Automate Cypress (UI component & E2E) tests

[othrayte]

To make the most use of our UI and E2E tests for the website we should automate their use in the CI pipeline, otherwise they won't stay working and aren't flagging issues.

As mentioned in our README for Cypress we should be able to automate the running of Cypress based tests as a CI step. That page mentions we should be able to do it for free, and after some very quick initial searches it looks like it might be free so long as we don't use Cypress Cloud, and publish screenshots etc as artifacts. Initial searching also found the official GitHub action.