## Why
Detached processor work can retain outgoing message senders, so waiting for
channel closure can keep the in-process app-server's outbound router alive
during shutdown.
## What changed
Add an explicit shutdown signal for the outbound router and prioritize it over
pending outgoing messages. Send that signal after processor tasks are stopped
so runtime shutdown no longer depends on every sender being dropped.
## Testing
Add a paused-time test that verifies the router exits and closes its channel
even when an outgoing sender is still retained.
GitOrigin-RevId: a8f88d88a0950f50339b1c56909fedb781f178d4