Already have provided 1 of many examples: classing. Applying a type to the communication relevant to the business

This is not an example. What type of communication? Are you classing emails? Are you classing internal documents? Are you classing marketing material? Are you classing internal comms?

To the process it could be scope, direction, decision ect. This can route, tag, extract, modify and move/copy messages automatically to target services

This description screams "use a proper ticketing system" to me but, again, I feel like I don't have enough information about the process you're talking about.

However jumping between apps is

A badly designed process or the wrong app.

So if someone can build an app like Outlook that has rich email, calendaring and pure depth of functionality that it has. This would be a massive barrier removal if not in my oppinion the last barrier for mass business FOSS adoption

Again, this all sounds like you guys are using the wrong tools for the job, but would need to hear more details.