Add integration tests for code host integrations

Created by: felixfbecker

We have integration tests for the webapp now, and the infrastructure for it is generic and resides in shared/: https://github.com/sourcegraph/sourcegraph/blob/master/shared/src/testing/integration/context.ts

The browser extension can use this the same way the webapp does to define tests similar to the current browser extension e2e tests. The browser extension would more heavily rely on HARs (not used in the webapp anymore) to record and replay responses from code hosts, since those are harder to define manually.

This is also blocked https://github.com/sourcegraph/sourcegraph/issues/12194 since there is not much to tests in the browser extension without it.