Fix Elastic migration tests that dirty the state

What does this MR do and why?

This resolves the flakiness so that the example doesn't have to be retried in a new process, but strangely the example only passes after an in-process retry (with rspec-retry), as can be seen at https://gitlab.com/gitlab-org/gitlab/-/jobs/3589555402#L839. Before the change, it would always fail: https://gitlab.com/gitlab-org/gitlab/-/jobs/3582322554.

I believe this is already an improvement, but it's still puzzling why the example only passes on retry.

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