refactor(youtube-player): simplify component internals (#27951)

The `youtube-player` component was set up to use long rxjs chains everywhere which made it difficult to reason about and unnecessarily complex. This complexity would've prevented us from adding new features to it.

These changes reduce the component by ~30% while preserving its behavior and making it easier to reason about.

(cherry picked from commit 3cbf125)

Author: crisbeto