Best way to unpublish a live app

Hi all,

I'm close to launch an application that is going to cannibalize with other applications I've right now.

To be honest I would like to know if there is a soft or good way to unpublish the old ones in order to force to migrate all my current users to the new app.

I know that unpublishing an app means that all devices with the installed app will continue having support.

Which are the next steps?
Unsuppor the Backend of the app?
Isn't that too hard for the user?
Isn't there any easy way?

Shall I add a feature to allow the user migrate his progress to the new app?

Greetings,
Nacho.