This reverts commit c2879cae2ee3707ad07af1118bf4862dc1d82bb7.
Additionally, we fix https://github.com/flutter/flutter/issues/40863 by adding a secondary VSYNC callback.
Unit tests are updated to provide VSYNC mocking and check the fix of https://github.com/flutter/flutter/issues/40863.
The root cause of having https://github.com/flutter/flutter/issues/40863 is the false assumption that each input event must trigger a new frame. That was true in the framework PR https://github.com/flutter/flutter/pull/36616 because the input events there are all scrolling move events. When the PR was ported to the engine, we can no longer distinguish different types of events, and tap events may no longer trigger a new frame.
Therefore, this PR directly hooks into the `VsyncWaiter` and uses its (newly added) secondary callback to dispatch the pending input event.
Additionally, we now use the engine directly as a delegate instead of storing potentially dead runtime_controller.
Unit tests have been updated to include an engine restart check which would fail before the fix.
This fixes https://github.com/flutter/flutter/issues/40303
