Sort and force grouping of includes (#4172)

This change enforces strict include grouping using IncludeCategories

In addition to adding this to the .clang-format file and applying it in the tests/src and src directories, I also did the following small changes:

    In ChatterSet.hpp, I changed lrucache to a <>include
    In Irc2.hpp, I change common/SignalVector.hpp to a "project-include"
    In AttachedWindow.cpp, NativeMessaging.cpp, WindowsHelper.hpp, BaseWindow.cpp, and StreamerMode.cpp, I disabled clang-format for the windows-includes
    In WindowDescriptors.hpp, I added the missing vector include. It was previously not needed because the include was handled by another file that was previously included first.
    clang-format minimum version has been bumped, so Ubuntu version used in the check-formatting job has been bumped to 22.04 (which is the latest LTS)

src/widgets/dialogs/BadgePickerDialog.cpp

@@ -1,10 +1,10 @@
 #include "BadgePickerDialog.hpp"
-#include <QSizePolicy>
-#include "singletons/Resources.hpp"
 
 #include "providers/twitch/TwitchBadges.hpp"
+#include "singletons/Resources.hpp"
 
 #include <QDialogButtonBox>
+#include <QSizePolicy>
 #include <QVBoxLayout>
 
 namespace chatterino {