Update Playwright tests for new ID legislation

[Bekabyx]

I had problems running Playwright on my machine and I exceeded a sensible timebox to get it working. This meant I couldn't update the e2e tests for the changes in PR #5275

Aside from issues running Playwright, I wasn't sure how to add tests which rely on new datasets because the way we use PW currently is based off of the legacy cassettes from when we used Harvest. I don't have knowledge of how these were generated or how to make new ones. @GeoWill has ideas on this: "I wonder if we can move to a mixture of mocking the API calls, and using HTTP Archive Files - which playwright seems to be set up to work with. (API mocking and HAR files docs)"