Why don't we use settings_testing for playwright tests?

[rebeccacremona]

Once #3081 lands, I don't see any reason why we shouldn't be able to use settings_testing for our playwright tests. Let's try it. (I could be missing something. Or it could be that we could be using them in CI now; I haven't given it much thought.) Primary motivation: I'd prefer for the playwright tests not to create persistent warcs. The current setup doesn't clean up after itself.