It works!

assets/pages/Container.vue

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+<template lang="html">
+  <ul ref="logs">
+    
+  </ul>
+</template>
+
+<script>
+let ws;
+export default {
+  props: ["id"],
+  name: "Container",
+  mounted() {
+    ws = new WebSocket(`ws://${window.location.host}/api/logs?id=${this.id}`);
+    ws.onopen = e => console.log("Connection opened.");
+    ws.onclose = e => console.log("Connection closed.");
+    ws.onerror = e => console.error("Connection error: " + e.data);
+    ws.onmessage = e => {
+      const parent = this.$refs.logs;
+      const item = document.createElement("li");
+      item.innerHTML = e.data;
+      parent.appendChild(item);
+    };
+  }
+};
+</script>
+<style>
+ul {
+  padding: 0;
+  margin: 0;
+}
+ul li {
+  list-style-type: none;
+}
+</style>

assets/pages/Index.vue

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+<template lang="html">
+  <div>
+    <ul>
+      <li v-for="item in containers">        
+        <router-link :to="{name: 'container', params: {id: item.Id}}">{{ item.Names[0] }} {{ item.Status}}</router-link>
+      </li>
+    </ul>
+  </div>
+</template>
+
+<script>
+export default {
+  name: "Index",
+  data() {
+    return {
+      containers: []
+    };
+  },
+  async created() {
+    this.containers = await (await fetch(`/api/containers.json`)).json();
+  }
+};
+</script>
+
+<style lang="css">
+</style>