Run tests with non-secret production flags turned on

[sarayourfriend]

Problem

The issue in https://github.com/WordPress/openverse-api/pull/682 could be prevented by CI if we ran the tests in at least the production configuration, if not in both the production and the current configuration.

Part of the issue is that of course our integration tests can't be run with throttling turned on or they'll fail. However, we should have some subset of tests (probably unit tests) that do run on the production-configured application.

Related to #680

Alternatives

Additional context

Implementation

• [ ] 🙋 I would be interested in implementing this feature.