I have been trying to join two file geodatabase tables in ArcGIS PRO 2.9.1 and getting an error "ERROR 160333 The table was not found" despite the tool running from within the APRX and the tables are clearly seen.
The solution to this problem was to run the arcpy.management.AddJoin() tool from within the python window after setting arcpy.env.workspace to the geodatabase containing the tables.