Add the applications menu to the dock

### Problem

Currently we have app launching split between two different processes on different sides of the screen. This requires those processes to communicate for things like pinning. Means duplicate code for any launcher features and they might get out of sync (like badges, context menus, drag behavior, rearranging, etc). Has complications with dragging launchers from the menu to the dock. Etc

### Proposal

Move the applications menu into the dock so we can recycle launcher code and make sure launchers behave the same in the dock and in the applications menu, maybe finally have re-arranging in the applications menu, at least make sure we have drag n drop easily between the applications menu and the dock without dragging across the whole screen

### Prior Art (Optional)

iPad OS:

GNOME Shell:

ChromeOS