fix(web): treat server clean close as session end without reconnect

Co-Authored-By: Claude <noreply@anthropic.com>

web/src/lib/api/process.ts

@@ -111,6 +111,7 @@ export function useProcessWebSocket(
   const reconnectTimeoutRef = useRef<number | null>(null);
   const intentionalCloseRef = useRef(false);
   const lastFrameWasExitRef = useRef(false);
+  const serverCleanCloseRef = useRef(false);
   const callbacksRef = useRef(new Set<(data: string) => void>());
 
   const clearReconnectTimeout = useCallback(() => {
@@ -157,6 +158,7 @@ export function useProcessWebSocket(
       ws.onopen = () => {
         reconnectAttemptsRef.current = 0;
         lastFrameWasExitRef.current = false;
+        serverCleanCloseRef.current = false;
         setStatus("open");
       };
 
@@ -171,9 +173,19 @@ export function useProcessWebSocket(
         callbacksRef.current.forEach((cb) => cb(data));
       };
 
-      ws.onclose = () => {
+      ws.onclose = (event) => {
         socketRef.current = null;
-        if (intentionalCloseRef.current || lastFrameWasExitRef.current) {
+        if (
+          (event.code === 1000 || event.code === 1001) &&
+          !intentionalCloseRef.current
+        ) {
+          serverCleanCloseRef.current = true;
+        }
+        if (
+          intentionalCloseRef.current ||
+          lastFrameWasExitRef.current ||
+          serverCleanCloseRef.current
+        ) {
           setStatus("closed");
           return;
         }