I haven't tested it myself yet, but Grapholite might do what you need, being better optimized for pen, though I don't think it is capable to automatically converts a sketch to models.
It got a free trial and full price is $40 dollar in the Microsoft store. Might give it a try myself upcoming week, need to do quite some diagramming myself.
Grapholite isn't free (https://grapholite.com/) but I found it easy and (importantly) flexible and a good value investment because I've used it for quite a lot of different technical communications over the years.
So I think what you are looking for is something with what we call swimlanes.
Across the top you (columns). That show the different "queues" or reports.
Then in the rows you have the different things.
So for the rows.
Email
Phone
Chat
Escalation
"Transfer " you can break this out into more specific items
Tech visit
Resolved
Customer survey
Columns "New" Assigned help desk Assigned level 2 Assigned level 3 Report Management etc.
So you drop boxes in there and point to the next "thing"
Example:
https://grapholite.com/ is worth a look too.... Does lots of mapping and flow diagrams etc..
Be interested to see your mileage with any of these. I have to confess that I found paper better, just found tech too restrictive for this kind of free flow thinking.