vue用watch监听路由的时候遇到的问题

Question

router.js代码

const routes = [
  {
    path: "/",
    name: "Home",
    component: Home,
    children: [
      {
        path: "/about",
        name: "About",
        component: () =>
          import( "../views/About.vue"),
      },
      {
        path: "/other",
        name: "Other",
        component: () =>
          import("../views/Other.vue"),
      }
    ],
  },
];

about.vue代码和other代码差不多就是名字改了

<template>
  <div class="about">
    <h1>This is an about page</h1>
  </div>
</template>

<script>
export default {
  data() {
    return {};
  },
  watch:{
    $route:function(to,from){
      console.log('about路由变化',to,from);
    }
  }
};
</script>

home.vue代码

<template>
  <div id="nav">
      <router-link :to="{path:'/about',query:{id:'123'}}">About</router-link>
      <router-link to="/other">Other</router-link>
      <router-view/>
  </div>
</template>
<script>
export default {
  name: 'Home',
  watch:{
    $route(){
      console.log('home路由变化');
    }
  }
}
</script>

运行结果及报错内容

点两个按钮去切换about和other路由无法输出是相应的路由变化，只会输出 home路由的变化

我想要达到的结果

在进入相应的页面的时候通过watch能监听到相应的路由变化 ，比如进入about会输出我上面写的about路由变化。就用watch监听
$route，不用组件内守卫