Enable emulator hotkeys and controller input (when that option is
enabled) when a TAS Input window has focus, as if it was the render
window instead.  This allows TASers to use frame advance and the like
without having to switch the focused window or disabling Hotkeys Require
Window Focus which also picks up keypresses while other apps are active.

Cursor updates are disabled when the TAS Input window has focus, as
otherwise the Wii IR widget (and anything else controlled by the mouse)
becomes unusable. The cursor continues to work normally when the render
window has focus.

qOverload is used to disambiguate pointers to overloaded functions, but
most of the usages in the code base were with non-overloaded functions.

Will manually controlling both an accelerometer and a gyroscope at the
same time be reasonable to do? No idea. Was this easy to implement
thanks to the input override system? Yes.

Fixes https://bugs.dolphin-emu.org/issues/12443.

IIRC we needed this before the input override system was added.

This gets rid of a blocking operation, improving performance and fixing
https://bugs.dolphin-emu.org/issues/12893.

This also makes us no longer directly access the state of certain UI
elements from the CPU thread, which probably wasn't thread-safe but
doesn't seem to have caused any observable issues so far.

This lets the TAS input code use a higher-level interface for
overriding inputs instead of having to fiddle with raw bits.
WiiTASInputWindow in particular was messy with how much
controller code it had to re-implement.

Fixes https://bugs.dolphin-emu.org/issues/12676.

Needs testing to see if this impacts performance when controller
inputs are changing.