seed: carry restart approval policy into new worlds

Make legacy core.exit share core.restart's supervisor gate and pending
request. Seed the stable agent prompt and boot comments with the approval
and shutdown contract, and check real init output under a deadline.
Cover both aliases' gate, response grace, coalescing and exit status.

Card: SAU-135

cli/src/host.rs

@@ -147,7 +147,7 @@ impl Host {
         )
         .await
     }
-    /// Wait until core.restart (after its response grace) or core.exit requests shutdown.
+    /// Wait until core.restart (or its alias core.exit) requests shutdown after its response grace.
     pub async fn exit_requested(&self) {
         let mut exit = self.0.exit.subscribe();
         let _ = exit.wait_for(|requested| *requested).await;