Improve exception logging of unobserved exceptions via FireAndForget

[peppy]

Coming from #27076, where the log output makes finding where the exception arrived for nigh impossible.

Example output:

2024-02-07 16:23:25 [error]: Unobserved exception via FireAndForget: Test
2024-02-07 16:23:25 [error]: System.InvalidOperationException: Test
2024-02-07 16:23:25 [error]: at osu.Game.Graphics.ScreenshotManager.<TakeScreenshotAsync>b__25_0() in /Users/dean/Projects/osu/osu.Game/Graphics/ScreenshotManager.cs:line 88
2024-02-07 16:23:25 [error]: at System.Threading.Tasks.Task`1.InnerInvoke()
2024-02-07 16:23:25 [error]: at System.Threading.ExecutionContext.RunFromThreadPoolDispatchLoop(Thread threadPoolThread, ExecutionContext executionContext, ContextCallback callback, Object state)
2024-02-07 16:23:25 [error]: --- End of stack trace from previous location ---
2024-02-07 16:23:25 [error]: at System.Threading.ExecutionContext.RunFromThreadPoolDispatchLoop(Thread threadPoolThread, ExecutionContext executionContext, ContextCallback callback, Object state)
2024-02-07 16:23:25 [error]: at System.Threading.Tasks.Task.ExecuteWithThreadLocal(Task& currentTaskSlot, Thread threadPoolThread)
2024-02-07 16:23:26 [debug]: Pressed (HoldForHUD) handled by HUDOverlay.
2024-02-07 16:23:26 [debug]: KeyDownEvent(ControlLeft, False) handled by GlobalActionContainer.
2024-02-07 16:23:26 [debug]: Pressed (Back) handled by HoldForMenuButton+HoldButton.
2024-02-07 16:23:26 [debug]: KeyDownEvent(Escape, False) handled by GlobalActionContainer.
2024-02-07 16:23:26 [debug]: Pressed (HoldForHUD) handled by HUDOverlay.
2024-02-07 16:23:26 [debug]: KeyDownEvent(ControlLeft, False) handled by GlobalActionContainer.
2024-02-07 16:23:26 [debug]: Pressed (Back) handled by HoldForMenuButton+HoldButton.
2024-02-07 16:23:26 [debug]: KeyDownEvent(Escape, False) handled by GlobalActionContainer.
2024-02-07 16:23:26 [debug]: Pressed (Back) handled by HoldForMenuButton+HoldButton.
2024-02-07 16:23:26 [debug]: KeyDownEvent(Escape, False) handled by GlobalActionContainer.
2024-02-07 16:23:27 [verbose]: ⚠️ Unobserved exception via FireAndForget: Test