fix(background-terminals): avoid false success after Windows taskkill timeout

extensions/background-terminals/src/manager.ts

@@ -395,11 +395,9 @@ export async function signalWindowsProcessTree(
       : attempt.outcome === "timed_out"
         ? `taskkill timed out after ${attempt.timeoutMs}ms; helper ${attempt.helperClosed ? "closed after SIGKILL" : `did not close within an additional ${attempt.helperCloseTimeoutMs}ms`}`
         : `taskkill exited ${attempt.exitCode ?? "without a code"}${attempt.signal ? ` (${attempt.signal})` : ""}`;
-  if (
-    attempt.outcome === "timed_out" &&
-    !attempt.helperClosed &&
-    !targetExited()
-  ) {
+  // Closing the helper or observing the shell exit does not prove that all
+  // descendants exited. Preserve uncertainty instead of killing only the shell.
+  if (attempt.outcome === "timed_out") {
     return { outcome: "unresolved", detail };
   }
   // A failed graceful taskkill must leave the shell PID alive for the

tests/extensions/background-terminals/manager.test.ts

@@ -204,6 +204,38 @@ test("Windows taskkill timeout waits for the stopped helper to close", async ()
   });
 });
 
+for (const signal of ["SIGTERM", "SIGKILL"] as const) {
+  for (const shellExitsDuringTimeout of [false, true]) {
+    test(`Windows ${signal} taskkill timeout stays unresolved when shell exit is ${shellExitsDuringTimeout}`, async () => {
+      let targetExited = false;
+      const killer = new EventEmitter() as ChildProcess;
+      killer.kill = () => {
+        targetExited = shellExitsDuringTimeout;
+        queueMicrotask(() => killer.emit("close", null, "SIGKILL"));
+        return true;
+      };
+      const signals: Array<NodeJS.Signals | number | undefined> = [];
+
+      const result = await signalWindowsProcessTree(
+        {
+          pid: 47,
+          kill(signal) {
+            signals.push(signal);
+            return true;
+          },
+        },
+        signal,
+        () => targetExited,
+        () => killer,
+      );
+
+      assert.equal(result.outcome, "unresolved");
+      assert.match(result.detail, /helper closed after SIGKILL/);
+      assert.deepEqual(signals, []);
+    });
+  }
+}
+
 test("Windows taskkill helper close has a second explicit bound", async () => {
   const killer = new EventEmitter() as ChildProcess;
   killer.kill = () => true;