As a tester, how do I know what has been rolled out to the test server at any one deployment?

Well, if the developers have been associating stories or tasks for stories with pull requests in Azure DevOps you should be able to reverse engineer what has been put forth. If you lead the name/note of a commit in git with the story number it will, by default, be the name of the pull request to be in Azure DevOps. This could help.