Currently analysis runtime information can be accessed programmatically using the AFSDK (AFAnalysisService.RuntimeInformationFields - https://techsupport.osisoft.com/Documentation/PI-AF-SDK/html/P_OSIsoft_AF_Analysis_AFAnalysisService_RuntimeInformationFields.htm). However, there are no fields which can be specified corresponding to backfilling/recalculation status of an analysis.
Adding a field for the aforementioned property or introducing a new method which could expose backfilling/recalculation status would be helpful for finding backfilling/recalculation errors programmatically. This approach should be much faster than finding analyses with backfilling errors in PSE.
The original request references AFAnalysisService.QueryRuntimeInformation Method, but I wonder if AFAnalysisService.QueueCalculation Method is more appropriate. The latter contains the remark, "This method queues the list of analyses on the analysis service service [sic] to be calculated. The operation is asynchronous and returning of the method does not indicate that queued analyses were calculated. The status can be queried in the upcoming releases using the returned handle."
This sounds like the requested functionality is planned but has not been implemented yet.