State: Avoid Global System Accessor

[mitaclaw]

No description provided.

[AdmiralCurtiss]

This isn't really deglobalizing anything, State.cpp still has global state that multiple instances of System would fight over.

[mitaclaw]

I see that PowerPC::Cache is accessing System through the global accessor, and can address that in another PR. Wiimote::DoState and Gecko::DoState I'm less confident I would know how to refactor those. Of course, the elephant in the room is g_video_backend participating in DoState. Still, isn't it a step in the right direction? I'm trying to bubble as many Core::System::GetInstance() uses up through functions until they reach the source of the problem, usually MainWindow.cpp, MainAndroid.cpp, or DolphinNoGUI.

[mitaclaw]

I just realized this PR conflicts with #12619 also authored by me. How I did that without noticing is beyond me. I think I will combine them under this PR.

[mitaclaw]

On closer inspection, I am unsure about simply copying the changes from #12619 because the s_load_or_save_in_progress_mutex currently is being locked before Core::RunOnCPUThread is called in SaveAs and LoadAs. I will be marking #12619 as a draft and leaving this PR as-is.