I want to register my Application (its a Gtk Application) to receive a signal when the user presses for example the "Next Song" Button, while it is not focused, so the User can change the playback while the Application remains in the background. I have no idea how to do this - will I need to include a specific Library for doing this on Ubuntu 18.04? Just to clarify: I am talking about System-Wide Hotkeys that applications can somehow intercept.
There isn't really a generic mechanism for this in Wayland (the security issues should be pretty obvious); for X, see the XGrabKey function.
For multimedia keys, there is a D-Bus interface you can use at org.gnome.SettingsDaemon.MediaKeys. For an example of how to use it, take a look at plugins/nmkeys/rb-mmkeys-plugin.c in Rhythmbox.