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.
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.