add process to mutate to Input component

apps/app/src/components/TreeItem/NewPageInput/use-new-page-input.tsx

@@ -1,7 +1,7 @@
 import React, { useState, type FC, useCallback } from 'react';
 
 import { createPage } from '~/client/services/page-operation';
-import { useSWRxPageChildren } from '~/stores/page-listing';
+import { useSWRxPageChildren, mutatePageTree } from '~/stores/page-listing';
 import { usePageTreeDescCountMap } from '~/stores/ui';
 
 import type { TreeItemToolProps } from '../interfaces';
@@ -9,6 +9,7 @@ import type { TreeItemToolProps } from '../interfaces';
 import { NewPageCreateButton } from './NewPageCreateButton';
 import { NewPageInput } from './NewPageInput';
 
+
 type UseNewPageInput = {
   Input: FC<TreeItemToolProps>,
   CreateButton: FC<TreeItemToolProps>,
@@ -76,6 +77,7 @@ export const useNewPageInput = (): UseNewPageInput => {
       });
 
       mutateChildren();
+      mutatePageTree();
 
       if (!hasDescendants) {
         stateHandlers?.setIsOpen(true);