Allow programmatic collection of timeline data

This was mentioned in https://github.com/Dart-Code/Dart-Code/issues/4106#issuecomment-1632883559. While debugging some analyzer performance issues I've been using the DevTools timeline and the `dart:developer` Timeline APIs to record events.

This works well, but there's a fair bit of manual work to connect DevTools, trigger the actions in the server, then fresh the timeline.

It would be really nice if I could call some APIs (for example in a test) that starts recording timeline data, executes a bunch of actions (that record timings using the Timeline APIs) and then dump to a file that can be opened in DevTools to review afterwards. This would make it easy to make very repeatable timings to evaluate changes.

I could imagine this also being useful for Flutter apps and tests. It could be neat if next to the Run/Debug links in VS Code above tests, there was a "Profile" (or similar) link, which runs the tests while capturing a trace, then opens the Timeline afterwards.

cc @kenzieschmoll