Fix write conflicts in parallel output

[nohwnd]

Replace instance lock with static lock, because there can be multiple different ThreadSafeStringWriters writing into the same async context. Reduce the locking only to state initialization and dictionary lookups and edits, but don't hold the lock over StringBuilder operations.

Add a wrapper for StringBuilder that locks on every method on the instance level, so when two threads get the same instance of StringBuilder then will sync together, but they won't sync with other threads that have different string builder.

Fix #1063

[nohwnd]

I've used the project from #1063 (comment) that @JustArchi so helpfully provided, and run it 100 times in a loop without error. And without any regression in execution time.

This might be slightly improved by locking only when we grab or initialize the State, and then making the edits on concurrent dictionary, but it adds more logic and I guess the improvements would be marginal.