## Why
New client requests and automatic continuations can start more work while the app-server is draining. Shutdown also needs to account for requests still preparing or submitting work before they appear as running turns.
## What changed
- Close a shared admission gate when shutdown begins, rejecting new turn work and thread lifecycle changes with the server-draining error.
- Apply the gate to automatic turn starts, including queued work and goal continuations, and recheck serialized turn requests before execution.
- Wait for admitted requests and running turns to finish, while preserving forced shutdown. Keep reads and `turn/interrupt` available during drain.
## Testing
Add coverage for admission permit tracking, discarded queued requests, forced shutdown, and WebSocket drain behavior, including request rejection, interruption, and suppression of automatic continuations.
GitOrigin-RevId: 1bc108aa00a427cfa41974fa9ec60754c2b968c2
