Handle initial message entirely within conditional

Towards #2065

Refactor the current implementation to reduce complexity and keep the
code for the current behavior within the condition body. This will allow
the new behavior to be implemented in another branch of the conditional.

- Remove the `readyCompleter`. Don't start listening on the server
  channel until the frame communication is ready instead of eagerly
  listening and holding the messages callbacks awaiting the ready
  future.
- Keep only the long-term message channel in the stored subscriptions.
  We only expect a single message on the window channel from each frame,
  so we can cancel the subscription after we receive it.