from your code, you use vue-cli, but why do you write all this in router/index.js?
isn't this the code you should write to import vue.js?

suppose you are using vue-cli, then your third-level component can be directly packaged into a separate component and imported into the secondary component, ha (the secondary component is imported by the first-level component)
can you understand what I mean? Then how do you realize the reuse of components when you use it this way, which is not in line with the core idea of vue-cli?

if you implement this way
Vue three-level routing nesting example
or you ide/essentials/nested-routes.html" rel= "nofollow noreferrer" > nested routing official documentation
why don't you try this?

children : [
          {
            path: 'childAccount',
            name: 'childAccount',
            meta: {
              icon:'ios-people',
              title: ''
            },
            component:() => import ('@/views/user-center'),
          },
          {path:'/', redirect: 'childAccount'}
        ]

make sure your path is right

see what error your console reported

{
    path : '/home',
    name : 'home',
    component : Main,
    meta : {
      menu: true,
      title: ''
    },
    children : [
      {
        path: 'account',
        name: 'account',
        redirect : '/home/account/childAccount',//
        component: () => import ('@/views/user-center/child-account'),
        meta: {
          icon:'ios-switch',
          title: ''
        },
        children : [
          {
            path: 'childAccount',
            name: 'childAccount',
            meta: {
              icon:'ios-people',
              title: ''
            },
            component:() => import ('@/views/user-center'),
          }
        ]
      }
   ]
 }

is the redirection wrong? write it as redirect:'/ home/account/childAccount', try

take a look at your console