Yellow squiggly lines begone!
Done automatically on .cpp files through `run-clang-tidy`, with manual corrections to the mistakes.
If an import is directly used, but is technically unnecessary since it's recursively imported by something else, it is *not* removed.
The tool doesn't touch .h files, so I did some of them by hand while fixing errors due to old recursive imports.
Not everything is removed, but the cleanup should be substantial enough.
Because this done on Linux, code that isn't used on it is mostly untouched.
(Hopefully no open PR is depending on these imports...)

By letting threads other than the host thread use things like
CPUThreadGuard, we can do a significant cleanup in AchievementsManager
in a later commit of this pull request.

Note: Some functions still can't be called from the CPU thread (or
threads the CPU thread might block on, like the GPU thread), but can
be called from any other thread.

PauseAndLock was only called with do_lock=true, and the function only
used unpauseOnUnlock when do_lock was false.

Replace calls of FifoManager::PauseAndLock(do_lock=false) with new
function RestoreState for clarity.

Host_RequestFullscreen and Host_UpdateMainFrame have been removed, and
Host_RequestRenderWindowSize has been used by DolphinQt since 80699096
and by Android since e8739156.

Remove Host_RefreshDSPDebuggerWindow (which hasn't done anything since
DolphinWX was removed in 44b22c90) and DSP::Host::UpdateDebugger (which
only called Host_RefreshDSPDebuggerWindow).

Remove Host_UpdateMainFrame(). The only non-empty call happened in
DolphinNoGUI which called s_update_main_frame_event.Set(), but
DolphinNoGUI never waits on that event.

Fix the following bug:

* Have a moveable ImGui overlay enabled, such as the Statistics window.
* Pause the game.
* Click and hold on the overlay's title bar as if you were going to move
  it. Because the screen isn't updating while the game is paused, you
  won't be able to actually move the overlay.
* Press the Frame Advance hotkey several times until it stops
  responding.

At this point emulation hotkeys are no longer responsive. This can be
resolved by selecting Play from the toolbar or menu, or selecting Frame
Advance from the menu a couple times, but it's annoying and not obvious
what's gone wrong or how to fix it.

Why the bug is happening:

* Doing a framestep while clicking on the overlay title bar causes ImGui
  to set IO.WantCaptureKeyboard to true, indicating that ImGui is
  requesting Dolphin ignore any keyboard events while the overlay is
  being interacted with.
* Dolphin complies with this request, causing
  Host_UIBlocksControllerState to return true and thus setting the input
  gate to ignore input.
* IO.WantCaptureKeyboard is only updated when ImGui::NewFrame() is
  called, which only happens at the end of each present. It thus remains
  true indefinitely since the game paused after the last framestep, and
  so Dolphin ignores any hotkeys such as the framestep or play keys.

The fix:

Ignore IO.WantCaptureKeyboard when the game is paused. ImGui can't
meaningfully capture input anyway when the game is paused, so this
shouldn't cause any problems elsewhere.

Once async presentation is implemented we'll want to revert this change,
both because it'll become unnecessary and because ImGui will be able to
do stuff while paused and so suppressing emulation hotkeys will actually
be useful.

There are two hard problems in computer science...