DevTools: Better linking between browser Performance tab and DevTools Profiler

Notes from a chat with Benoit:

It would be nice if starting profiling (or reload and profiling) in the browser auto-started profiling in DevTools.

It would also be nice if viewing a range of time in the Performance tab narrowed down the commits within the Profiler. At least starting the profilers at the same time would enable a manual match-up.

To my knowledge, none of the currently available APIs (including experimental) would enable us to support this level of integration.

If we were to make use of the DevTools protocol, we could Profiler.start and Profiler.stop the built-in profiler in sync with React's own profiler. Chrome's profiler also dispatches Profiler.consoleProfileStarted and Profiler.consoleProfileFinished events which we could use to follow the browser's profiler if we wanted to.

There do not appear to be any APIs/events for syncing the zoomed-in range.

Originally reported via https://github.com/bvaughn/react-devtools-experimental/issues/37

Start by reviewing the DevTools Protocol Profiler.start and Profiler.stop methods and the Profiler.consoleProfileStarted and Profiler.consoleProfileFinished events mentioned in the issue. Determine whether current browser APIs can support synchronized React and browser profiling and Performance-tab range linking; done means a defined, working integration or a documented API limitation.