feat: add heartbeat/ping to terminal WebSocket

- Backend: Send ping every 30s from WebSocket endpoint
- Frontend: Respond to pings with pongs, detect missed pings (60s timeout)
- Update type definitions to include 'resetting' status

Refs: persistent-terminal-sessions task 6.4

apps/web/src/components/mobile-terminal-header.tsx

@@ -8,7 +8,7 @@ interface MobileTerminalHeaderProps {
   onClose?: () => void;
   onFontSizeChange?: (delta: number) => void;
   isVisible: boolean;
-  connectionStatus?: "connecting" | "connected" | "disconnected" | "error";
+  connectionStatus?: "connecting" | "connected" | "disconnected" | "error" | "resetting";
 }
 
 export const MobileTerminalHeader: React.FC<MobileTerminalHeaderProps> = ({

apps/web/src/components/mobile-terminal-wrapper.tsx

@@ -30,7 +30,7 @@ export const MobileTerminalWrapper: React.FC<MobileTerminalWrapperProps> = ({
   const [activeModifier, setActiveModifier] = useState<ModifierKey | null>(null);
   const [terminalRef, setTerminalRef] = useState<{
     sendData: (data: string) => void;
-    connectionStatus: "connecting" | "connected" | "disconnected" | "error";
+    connectionStatus: "connecting" | "connected" | "disconnected" | "error" | "resetting";
     focusInput: () => void;
     changeFontSize: (delta: number) => void;
   } | null>(null);
@@ -42,7 +42,7 @@ export const MobileTerminalWrapper: React.FC<MobileTerminalWrapperProps> = ({
   }, [headerAutoHide]);
 
   const handleTerminalReady = useCallback(
-    (sendData: (data: string) => void, connectionStatus: "connecting" | "connected" | "disconnected" | "error", focusInput: () => void, changeFontSize: (delta: number) => void) => {
+    (sendData: (data: string) => void, connectionStatus: "connecting" | "connected" | "disconnected" | "error" | "resetting", focusInput: () => void, changeFontSize: (delta: number) => void) => {
       setTerminalRef({ sendData, connectionStatus, focusInput, changeFontSize });
     },
     []

apps/web/src/components/terminal.tsx

@@ -14,7 +14,7 @@ interface TerminalProps {
   onModifierChange?: (modifier: ModifierKey | null) => void;
   onTerminalReady?: (
     sendData: (data: string) => void,
-    connectionStatus: "connecting" | "connected" | "disconnected" | "error",
+    connectionStatus: "connecting" | "connected" | "disconnected" | "error" | "resetting",
     focusInput: () => void,
     changeFontSize: (delta: number) => void
   ) => void;
@@ -54,6 +54,8 @@ export const TerminalComponent: React.FC<TerminalProps> = ({
     const stored = localStorage.getItem(FONT_SIZE_KEY);
     return stored ? parseInt(stored, 10) : isMobile ? 16 : 14;
   });
+  const lastPingRef = useRef<number>(0);
+  const heartbeatCheckRef = useRef<number | null>(null);
 
   const calculateFontSize = useCallback(() => {
     if (!isMobile) return fontSize;
@@ -75,6 +77,20 @@ export const TerminalComponent: React.FC<TerminalProps> = ({
       setStatus("connected");
       setError(null);
       reconnectAttemptsRef.current = 0;
+      lastPingRef.current = Date.now();
+      
+      // Start heartbeat check
+      if (heartbeatCheckRef.current) {
+        window.clearInterval(heartbeatCheckRef.current);
+      }
+      heartbeatCheckRef.current = window.setInterval(() => {
+        const elapsed = Date.now() - lastPingRef.current;
+        if (elapsed > 60000) {
+          // No ping for 60 seconds, connection may be dead
+          console.warn("Terminal heartbeat timeout, reconnecting...");
+          ws.close(4000, "Heartbeat timeout");
+        }
+      }, 30000);
     };
 
     ws.onmessage = (event) => {
@@ -95,6 +111,12 @@ export const TerminalComponent: React.FC<TerminalProps> = ({
             } else if (msg.status === "resetting") {
               setStatus("resetting");
             }
+          } else if (msg.type === "ping") {
+            // Respond with pong and update last ping time
+            lastPingRef.current = Date.now();
+            if (ws.readyState === WebSocket.OPEN) {
+              ws.send(JSON.stringify({ type: "pong" }));
+            }
           }
         } catch {
           termRef.current?.write(event.data);
@@ -104,6 +126,13 @@ export const TerminalComponent: React.FC<TerminalProps> = ({
 
     ws.onclose = (event) => {
       setStatus("disconnected");
+      
+      // Clean up heartbeat check
+      if (heartbeatCheckRef.current) {
+        window.clearInterval(heartbeatCheckRef.current);
+        heartbeatCheckRef.current = null;
+      }
+      
       if (event.code !== 1000) {
         setError(`Connection closed (code: ${event.code})`);