Playwright (e2e-tests) for v3 apps

[framitdavid]

Why: Although our primary focus remains on enriching Studio with new functionality, we also have a responsibility to ensure that apps using v3 can still be configured within Studio. We may need to support v3 apps for configuration for up to a year, if not longer.

Some endpoints are shared between v3 and v4 in the designer backend. Therefore, it's crucial to catch errors for v3 apps if we make changes for v4 that might affect v3. We're striving to separate dependencies to make it easier to remove v3 code when we no longer need to support. However, we don't always catch these dependencies manually, which is why we require automated tests to assist us.

What: Vi må implementere Playwright (e2e-tester) for v3 som sørger for at de viktigste funksjonene fungerer. Istedenfor å skrive alle testene på nytt, foreslår jeg at man går tilbake I git historikken og henter ut e2e-testene for v3-apper. Vi må også large en v3 app som alltid får level I ttd, so vi kan tested mot.

### Playwrigth (e2e-tests)
- [ ] Use the git history to extract the v3 tests and verify that they meet the regression test criteria
- [ ] Ensure that the tests are running on every PR (that has changed relevant code)