Do I need to zip up each as a separate shapefile or can I add multiple to a file geodatabase then zip that up?
You are correct. The easiest way to add multiple layers as an item to AGOL would be to add them to a file geodatabase and zip it up.
What can you add to ArcGIS Online?—ArcGIS Online Help | ArcGIS
I would prefer to use the share option in ArcGIS Pro (or ArcMap). Introduction to sharing web layers—ArcGIS Pro | ArcGIS Desktop
Retrieving data ...