fix(web): address the review round on the one-route add flow

- lifecycle-chrome's second scaffold staged its workspace under the OUTER
  scaffold's temp root, coupling two supposedly independent worlds and
  leaving the aria scrub root wrong; it now uses its own workspaceCwd.
- The direct-open path now carries the same `flowBusy` gate that disables
  the equivalent menu entry, so an occupant re-registering mid-adoption
  cannot raise a second flow.
- A composition with no directory-picker no longer opens a zero-entry
  popover on the hero anchor: with nothing to pick and nothing to add,
  the gesture shows nothing. Both behaviors gain a unit test.
- Brought three partially superseded Agent Notes current (the native
  picker, the workspace UI product flow, and the sidebar browsing split),
  cross-linked to this decision, both languages re-recorded.
- Corrected this Note's own Testing section: the shared e2e helper stages
  and adopts its directory, it does not create one in-dialog — only
  workspace-management does. Named the client-seam and CLI-README residue
  in the follow-up TODO alongside the wire branch.

packages/client/ui-workspace/src/client/WorkspacePicker.tsx

@@ -114,6 +114,10 @@ export function WorkspacePickFlow({
       disabled: flowBusy,
     }))
     : addEntries
+  // Nothing listed and nothing to add with (a composition that mounts this
+  // package without any directory-picker): an empty popover would claim a
+  // choice that does not exist, so the anchor gesture shows nothing at all.
+  const menuIsEmpty = items.length === 0
 
   const closeModal = (): void => {
     setErrorOpen(false)
@@ -153,9 +157,11 @@ export function WorkspacePickFlow({
   // made unnecessary; the add-only surface lists nothing and never waits.
   const listSettled = addOnly || workspaceSnapshot.phase === 'ready'
   const addIsTheOnlyEntry = !pinAdd && listSettled && addEntries.length === 1
+  // `flowBusy` gates this exactly as it disables the equivalent menu entry: a
+  // pick still being adopted owns the surface until it settles.
   useEffect(() => {
-    if (open && addIsTheOnlyEntry) openDirectoryFlow()
-  }, [open, addIsTheOnlyEntry, openDirectoryFlow])
+    if (open && addIsTheOnlyEntry && !flowBusy) openDirectoryFlow()
+  }, [open, addIsTheOnlyEntry, flowBusy, openDirectoryFlow])
 
   /** Owner side of the flow conversation: adopt keeps the flow open (busy) until the Host answers. */
   const flowOwner: DirectoryFlowOwnerProps = {
@@ -185,7 +191,7 @@ export function WorkspacePickFlow({
   return (
     <>
       <Menu
-        open={open && !addIsTheOnlyEntry}
+        open={open && !addIsTheOnlyEntry && !menuIsEmpty}
         anchor={null}
         items={items}
         {...pinAdd ? { footer: addEntries } : {}}
@@ -196,7 +202,7 @@ export function WorkspacePickFlow({
         portal
         getAnchorRect={getAnchorRect}
       />
-      {open && !addIsTheOnlyEntry && workspaceSnapshot.phase === 'pending' && <div className={css.menuStatus} role="status">{t('picker.loading')}</div>}
+      {open && !addIsTheOnlyEntry && !menuIsEmpty && workspaceSnapshot.phase === 'pending' && <div className={css.menuStatus} role="status">{t('picker.loading')}</div>}
       {renderDirectoryFlow(flowOwner)}
       <Modal
         open={errorOpen}

packages/client/ui-workspace/tests/workspace-picker.spec.tsx

@@ -253,6 +253,34 @@ describe('WorkspacePicker', () => {
     expect(screen.getByRole('menuitem', { name: '添加工作区…' })).toBeTruthy()
   })
 
+  it('shows no popover at all when nothing is listed and nothing can be added', () => {
+    // A composition mounting this package without any directory-picker: the
+    // hero anchor has neither a Workspace to pick nor a way to add one, so it
+    // must not claim a choice with an empty menu.
+    const b = mount([], vi.fn(), occupancySource(false))
+    expect(screen.queryByRole('menu')).toBeNull()
+    expect(screen.queryByTestId('directory-flow')).toBeNull()
+    expect(b.createWorkspace).not.toHaveBeenCalled()
+  })
+
+  it('holds the anchor gesture while an adoption is still settling', async () => {
+    // The auto-open path obeys the same busy rule as the disabled menu entry:
+    // an occupant that re-registers mid-adoption must not raise a second flow.
+    let resolve!: (workspace: WorkspaceView) => void
+    const pending = new Promise<WorkspaceView>((settle) => { resolve = settle })
+    const created = workspace('adopted')
+    const b = mount([workspace('alpha', 'Alpha')], vi.fn(() => pending))
+    chooseAdd()
+    act(() => { b.probe.owner!.onPicked('/tmp/project') })
+    expect(b.probe.owner!.busy).toBe(true)
+    // The list empties under the still-settling adoption (the workspace was
+    // deleted elsewhere), which would otherwise make add the only entry.
+    act(() => { b.rerenderItems([]) })
+    expect(b.createWorkspace).toHaveBeenCalledTimes(1)
+    await act(async () => { resolve(created); await pending })
+    expect(b.probe.owner!.busy).toBe(false)
+  })
+
   it('hides the add entry while the directory-flow hole is empty', () => {
     mount([workspace('alpha', 'Alpha')], vi.fn(), occupancySource(false))
     expect(screen.getByRole('menuitem', { name: 'Alpha' })).toBeTruthy()

packages/host/apiproxy/src/api-proxy.ts

@@ -1594,8 +1594,12 @@ export function createApiProxy(ctx: Context, defaults: ApiProxyDefaults): ApiPro
       // TODO: the create-by-name branch lost its last product consumer when
       // the Web picker collapsed onto the directory flow
       // (.agents/notes/implemented/simplification/2026-07-31-one-route-to-add-a-workspace.md).
-      // Delete it with the wire schema's `name` member, this `defaults.workspaceRoot`,
-      // and the `dsh web --workspace-root` flag that exists only to feed it.
+      // Delete it with the wire schema's `name` member, this
+      // `defaults.workspaceRoot`, the client seam that carried the name
+      // (`WorkspaceCreateInput`, `WorkspacesService.create`'s `{ name }` arm,
+      // `intentName`'s name branch, the manager's "name under workspaceRoot"
+      // contract), and the `dsh web --workspace-root` flag plus its apps/cli
+      // README lines, which exist only to feed it.
       async create(request) {
         const { payload } = request
         let path: string