A little late in responding, but wanted to provide a solution in case anyone else has a similar issue. The most common scenario is to stop the entire test run or prevent it from executing if the first test fails...
Since Azure ignores the onLogError attempts to force Runner.Stop(), the simple solution would be to break this 1st test into it's own pipeline task. Then the subsequent task that runs the remaining tests can be configured to execute only when all previous tasks have succeeded.
Another possible approach is to not use test adapter but start TestExecute via command line task. In this case TestExecute will have full control over project's Execution Plan and will be able to honor its OnError/OnException settings.
