nuxt auth v5 not setting loggedin when use login & logout

Question

when user logging in, the this.$auth.$state.loggedIn value stay false and when reload the page it's work

also when user logging out, the this.$auth.$state.loggedIn value stay true and when reload the page it's work

this is my nuxt.config.js:

auth: {
    rewriteRedirects: false,
    redirect: {
      login: '/login',
      logout: '/',
      callback: false,
      home: false
    },
    strategies: {
      local: {
        token: {
          property: 'auth_token',
          global: true,
          required: true,
          type: 'Bearer',
          maxAge: 60 * 60 * 24 * 30 * 12 * 70
        },
        user: {
          property: false
        },
        endpoints: {
          login: { url: '/v1/token/login/', method: 'post' },
          logout: false,
          user: { url: '/v1/user', method: 'get' }
        }
      }
    }
  }

and login function:

const login = await this.$auth.loginWith('local', {
              data: userData
            }).catch((err) => {
              if (!err.response) { return }
              console.log(err)

              switch (err.response.status) {
                case 403:
                  this.error = 'Incorrect username/password'
                  break
                case 401:
                  this.error = 'Incorrect username/password'
                  break
                case 417:
                  this.error = 'Unauthorized.'
                  break
                default:
                  this.error = 'Something Wrong Happend'
                  break
              }
            })

and logout function:

async onLogout () {
      await this.$auth.logout()
      this.$nuxt.$router.push('/')
    }

nuxt versiom: "^2.15.3" @nuxtjs/auth-next versiom: "5.0.0-1648802546.c9880dc"