For Work Type:

Go to the sidebar work. Select all work and get rid of all filters and then turn it into a list instead of a kanban. One column will be work type (if not, you can add). Then you can sort by work type. 

You can also filter by work type, so if you want your kanban view of just a certain work type you can do that. 

I don’t think there is anything for task type though? 

This is the answer

I don’t believe there is any report available in Karbon itself by Task Type, but you may be able to get what you need using Karbon Practice Intelligence (see Intelligence tab in Karbon)

Thank you David Sadowsky! This was very helpful!