Reland "Fix the first frame logic in tracing and driver (#35297)" (#37192)

This relands https://github.com/flutter/flutter/pull/35297

The followings have been done to fix the broken tests:
  1. Add `didSendFirstFrameRasterizedEvent` extension and its tests
  2. Wait for `didSendFirstFrameRasterizedEvent` instead of
     `didSendFirstFrameEvent` during start up tests
  3. Mark missed (probably newly added) start up tests as flaky