AudioCommon: Remove lock on Pause state

[degasus]

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.

[dolphin-emu-bot]

FifoCI detected that this change impacts graphical rendering. Here are the behavior differences detected by the system:

• fog-adj on dx-win-nv: failed to render

_{^{automated-fifoci-reporter}}

[delroth]

LGTM. Locking does not make much sense here -- we don't have anything to save in terms of state in the mixer.