cmux-tui: simplify JoinSet shutdown drains

cmux-tui/crates/chatmux-relay/src/preview_proxy.rs

@@ -474,8 +474,7 @@ async fn spawn_proxy(target_port: u16, ring: Arc<ConsoleRing>) -> Result<ProxyRu
                 }
             }
         }
-        connections.abort_all();
-        while connections.join_next().await.is_some() {}
+        connections.shutdown().await;
         let upgrades = shared
             .upgrades
             .lock()

cmux-tui/crates/cmux-remote/src/bridge.rs

@@ -30,8 +30,7 @@ impl ForwardConnections {
 
     async fn shutdown(&self) {
         let mut tasks = self.tasks.lock().await;
-        tasks.abort_all();
-        while tasks.join_next().await.is_some() {}
+        tasks.shutdown().await;
     }
 
     fn abort_all(&self) {
@@ -205,8 +204,7 @@ pub async fn serve_mux_bridge(
             }
         }
     }
-    connections.abort_all();
-    while connections.join_next().await.is_some() {}
+    connections.shutdown().await;
 }
 
 #[derive(Debug, Default, PartialEq, Eq)]

cmux-tui/crates/cmux-remote/src/services.rs

@@ -330,8 +330,7 @@ impl DaemonServices {
             }
         }
         self.workspace.shutdown().await;
-        handlers.abort_all();
-        while handlers.join_next().await.is_some() {}
+        handlers.shutdown().await;
         self.workspace.shutdown().await;
     }