video_core didn't even properly use them, and they were the source of
many otherwise-unnecessary dependencies from core to video_core.

1. removed zl, zr and c-stick from HID::PadState. They are handled by IR, not HID
2. removed button handling in EmuWindow
3. removed key_map
4. cleanup #include

More ergonomic to use and will be required for upcoming changes.

* Removes circular dependences (common should not depend on core)

Allows users to choose a single screen layout or a large screen layout.
Adds a configuration option to change the prominent screen.

This makes clang-format useful on those.

Also add a bunch of forgotten transitive includes, which otherwise
prevented compilation.

If the mouse position for a mouse move/drag would take it outside the emulated screen dimensions, clip the coordinates to
the emulated screen dimensions.
Qt and GLFW will report negative coordinates for mouse positions to the left, or above citra window. Added restriction
to mouse coordinates passed to touchmoved by Qt/GLFW to be greater or equal to zero.