.NET integration tests work locally, but not on codebuild

**Describe the bug**
We need to fix .NET integration tests working on codebuild.
For some reason, despite installing the omnisharp extension, codelenses never show up and the test fails. There is nothing output during this time: we need to figure out how to pull logs from the debug menu in a headless instance.
To make sure that we are testing everything we need to, we need to figure out what is going wrong and fix it.

Start by reproducing the .NET integration-test failure in CodeBuild and investigate why the OmniSharp codelenses do not appear in the headless instance. Determine how to retrieve debug-menu logs, then verify that the affected integration tests run successfully in CodeBuild with useful failure output.

Written by the indexing model from the issue text.