The triangles intro tracks video time, which is not adjusted based on
the game's playback rate (ie. it runs in realtime even for headless
tests).
Maybe we want to make the triangles video adjust its rate along with
tests?
Closes#14762.
This class is ugly. I think the whole process should be clened up once
we have correctly-scheduled `SynchronizationContext`s. There's not much
saving it as long as all these interdispersed `Schedule`s around
required.