"homey:manager:api") allows an app to access the Homey Web API. This web api can be used to control all of Homey (devices, Flows, etc) even if they are not part of the App that requested the permission. This level of access can be used to add new advanced functionality to Homey. However because an app receives complete control over the Homey it is installed on this permission should only be requested when it is the main functionality of your app.
homey:app:<appId>, where the
appIdis that of the app you want to communicate with. For example