Code Insights: Add integration test for dashboard crud operations

Created by: vovakulikov

Closes https://github.com/sourcegraph/sourcegraph/issues/34001

In this PR we cover the dashboard test with integration tests. We didn't use unit test because our units at the moment are strictly bound to concrete implementation and it might be a problem in future when we will have a big shift in GQL/API paradigm in the near future. I wish we had more unit tests tooling around code insights logic but unfortunately, we don't have it at the moment.

Test plan

• Make sure that CI is green and the integration tests work properly

App preview:

• Web
• Storybook

Check out the client app preview documentation to learn more.