What object type are you reporting on? I know for a project, task, or issue report, you can only get the information on the default baseline and not all baselines.
If you use a baseline report, you do see the different baselines (set a filter or use a prompt for Project ID). I have attached a screenshot of the fields from the API explorer so you can see what options you have. You do not get a screenshot though of who was assigned the task at the time of the baseline. I get that request all the time and unfortunately cannot help them out.
To see the "official list", you can go to the API explorer and look at the