Search integration tests cause a lot of log spam errors and are sometimes flaky

Created by: felixfbecker

The search integration tests still seem to contain many various unmocked responses. See for example: https://buildkite.com/sourcegraph/sourcegraph/builds/76962#5d7602d6-7940-409d-8bf1-e402d68b63fc/112-223 This makes the tests very hard to debug because you have to scroll past a lot of logs (that may very well be relevant!) and it's hard to distinguish the red herrings.