AudioCommon: Remove lock on Pause state

We had to lock audiocommon with the old asynchron HLE audio emulation,
now our Mixer is just a plain FIFO which may underrun.
Of course, this will stutter, but underruning the audio backend is likely worse.

Source/Core/AudioCommon/Mixer.h

@@ -108,8 +108,6 @@ public:
 		}
 	}
 
-	std::mutex& MixerCritical() { return m_csMixing; }
-
 	float GetCurrentSpeed() const { return m_speed.load(); }
 	void UpdateSpeed(float val) { m_speed.store(val); }
 
@@ -155,7 +153,5 @@ protected:
 	bool m_log_dtk_audio;
 	bool m_log_dsp_audio;
 
-	std::mutex m_csMixing;
-
 	std::atomic<float> m_speed; // Current rate of the emulation (1.0 = 100% speed)
 };