DolphinQt: Rework TAS input threading, part 1 (buttons)

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.

Source/Core/DolphinQt/TAS/TASInputWindow.h

@@ -79,6 +79,5 @@ private:
   std::optional<ControlState> GetSpinBox(QSpinBox* spin, u16 zero, ControlState controller_state,
                                          ControlState scale);
 
-  std::map<TASCheckBox*, bool> m_checkbox_set_by_controller;
   std::map<QSpinBox*, u16> m_spinbox_most_recent_values;
 };