fix(approval): log + evict on failed approval broadcast (S4)

broadcast() wrapped each client.send in a bare runCatching with no logging or
dead-client eviction, so an approval prompt could vanish silently and the session
hang until reconnect. Now log+evict failed clients from both registries and error
when a prompt reaches 0 live clients.

Note: :apps:server:test not run (core:kernel temporarily broken by concurrent work);
change is isolated, compiled clean before the breakage, detekt passes.

apps/server/src/main/kotlin/com/correx/apps/server/approval/ApprovalCoordinator.kt

@@ -13,6 +13,7 @@ import com.correx.core.events.types.SessionId
 import com.correx.core.kernel.orchestration.ApprovalGateway
 import io.ktor.server.websocket.DefaultWebSocketServerSession
 import io.ktor.websocket.Frame
+import org.slf4j.LoggerFactory
 import java.util.concurrent.ConcurrentHashMap
 
 open class ApprovalCoordinator(
@@ -117,8 +118,29 @@ open class ApprovalCoordinator(
         val encoded = ProtocolSerializer.encodeServerMessage(msg)
         val sessionSubs = sessionClients[sessionId].orEmpty()
         val recipients: Set<DefaultWebSocketServerSession> = sessionSubs + globalClients
+        var delivered = 0
         recipients.forEach { client ->
             runCatching { client.send(Frame.Text(encoded)) }
+                .onSuccess { delivered++ }
+                .onFailure { err ->
+                    // A dead socket must not silently swallow an approval prompt. Log it and evict
+                    // the client from both registries so we don't keep sending into a closed socket
+                    // (the client re-registers and gets the pending approval from the snapshot on
+                    // reconnect).
+                    log.warn("approval broadcast to a client failed, evicting: {}", err.message)
+                    sessionClients[sessionId]?.remove(client)
+                    globalClients.remove(client)
+                }
+        }
+        if (delivered == 0) {
+            log.error(
+                "approval prompt for session={} reached 0 live clients; session stays paused until a client reconnects",
+                sessionId.value,
+            )
         }
     }
+
+    private companion object {
+        private val log = LoggerFactory.getLogger(ApprovalCoordinator::class.java)
+    }
 }