Fix race condition in TestDockerCommandWithRunnerServiceEnvironmentVariables

Timo Furrerrequested to merge
fix-race-condition-docker-int into main

What does this MR do?

Fix race condition in TestDockerCommandWithRunnerServiceEnvironmentVariables

This fixes a race condition that happens a lot in CI. I attribute this to the same as was recently the case with TestDockerServiceHealthcheckOverflow and fixed with !5985 (merged).

Use that MR description for context on the cause and fix for this race condition.

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