feat(HAI-049): add recycleWorktrees checkbox to Settings modal

- Add recycleWorktrees toggle to the Worktrees section in SettingsModal
- Wire checkbox state to settings store
- Add unit tests for recycleWorktrees setting behavior

packages/dashboard/app/components/SettingsModal.tsx

@@ -26,7 +26,7 @@ interface SettingsModalProps {
 }
 
 export function SettingsModal({ onClose, addToast }: SettingsModalProps) {
-  const [form, setForm] = useState<Settings & { worktreeInitCommand?: string }>({ maxConcurrent: 2, maxWorktrees: 4, pollIntervalMs: 15000, groupOverlappingFiles: false, autoMerge: false, worktreeInitCommand: "" });
+  const [form, setForm] = useState<Settings & { worktreeInitCommand?: string }>({ maxConcurrent: 2, maxWorktrees: 4, pollIntervalMs: 15000, groupOverlappingFiles: false, autoMerge: false, recycleWorktrees: false, worktreeInitCommand: "" });
   const [loading, setLoading] = useState(true);
   const [activeSection, setActiveSection] = useState<SectionId>(SETTINGS_SECTIONS[0].id);
 
@@ -150,6 +150,20 @@ export function SettingsModal({ onClose, addToast }: SettingsModalProps) {
               />
               <small>Shell command to run in each new worktree after creation</small>
             </div>
+            <div className="form-group">
+              <label htmlFor="recycleWorktrees" style={{ display: "flex", alignItems: "center", gap: "8px" }}>
+                <input
+                  id="recycleWorktrees"
+                  type="checkbox"
+                  checked={form.recycleWorktrees}
+                  onChange={(e) =>
+                    setForm((f) => ({ ...f, recycleWorktrees: e.target.checked }))
+                  }
+                />
+                Recycle worktrees
+              </label>
+              <small>When enabled, completed task worktrees are returned to an idle pool instead of being deleted, preserving build caches for faster startup</small>
+            </div>
           </>
         );
       case "commands":

packages/dashboard/app/components/__tests__/SettingsModal.test.tsx

@@ -9,6 +9,7 @@ const defaultSettings: Settings = {
   pollIntervalMs: 15000,
   groupOverlappingFiles: false,
   autoMerge: false,
+  recycleWorktrees: false,
   worktreeInitCommand: "",
   testCommand: "",
   buildCommand: "",
@@ -75,6 +76,7 @@ describe("SettingsModal", () => {
     fireEvent.click(screen.getByText("Worktrees"));
     expect(screen.getByLabelText("Max Worktrees")).toBeTruthy();
     expect(screen.getByLabelText("Worktree Init Command")).toBeTruthy();
+    expect(screen.getByText("Recycle worktrees")).toBeTruthy();
 
     // Commands
     fireEvent.click(screen.getByText("Commands"));
@@ -86,6 +88,31 @@ describe("SettingsModal", () => {
     expect(screen.getByText("Auto-merge completed tasks")).toBeTruthy();
   });
 
+  it("shows Recycle worktrees checkbox in Worktrees section", async () => {
+    render(<SettingsModal onClose={onClose} addToast={addToast} />);
+    await waitFor(() => expect(fetchSettings).toHaveBeenCalled());
+
+    fireEvent.click(screen.getByText("Worktrees"));
+    const checkbox = screen.getByLabelText("Recycle worktrees");
+    expect(checkbox).toBeTruthy();
+    expect(checkbox.getAttribute("type")).toBe("checkbox");
+  });
+
+  it("toggling recycleWorktrees checkbox sends true in save payload", async () => {
+    render(<SettingsModal onClose={onClose} addToast={addToast} />);
+    await waitFor(() => expect(fetchSettings).toHaveBeenCalled());
+
+    fireEvent.click(screen.getByText("Worktrees"));
+    const checkbox = screen.getByLabelText("Recycle worktrees");
+    fireEvent.click(checkbox);
+
+    fireEvent.click(screen.getByText("Save"));
+    await waitFor(() => expect(updateSettings).toHaveBeenCalledTimes(1));
+
+    const payload = (updateSettings as ReturnType<typeof vi.fn>).mock.calls[0][0];
+    expect(payload.recycleWorktrees).toBe(true);
+  });
+
   it("groupOverlappingFiles input has type checkbox", async () => {
     render(<SettingsModal onClose={onClose} addToast={addToast} />);
     await waitFor(() => expect(fetchSettings).toHaveBeenCalled());