Here's how to do with createApp in Vue 3, but the context (stores, plugins, directives...) will not be kept.

Copy// DialogService.js
import { createApp } from 'vue';

export default {
  alert(text) {
    const mountEl = document.createElement('div');
    document.body.appendChild(mountEl);

    const dialog = createApp({ extends: DialogComponentDef }, {
      // props
      text,
      // events are passed as props here with on[EventName]
      onClose() {
        mountEl.parentNode.removeChild(mountEl);
        dialog.unmount();
        dialog = null;
      },
    });

    dialog.mount(mountEl);
  },
};

To keep the context, there's something more complicated that can be seen here with h and render Vue methods : https://github.com/vuejs/vue-next/issues/2097#issuecomment-709860132

It turns out that Vue has <component :is="yourComponentType"> which does exactly what I was hoping to accomplish if you throw it into a v-for loop. Documents here.

1) Since you're manually instantiating that component and it doesn't belong to your main app's component tree, the store won't be automatically injected into it from your root component. You'll have to manually provide the store to the constructor when you instantiate the component ..

import ProjectRow from "./ProjectRow.vue";
import Vue from "vue";
import store from "../store";

let ProjectRowClass = Vue.extend(ProjectRow);
let ProjectRowInstance = new ProjectRowClass({ store });

2) In a Vue Single File Component (SFC), outside of the default export this doesn't refer to the Vue instance, so you don't have access to $refs or any other Vue instance property/method. To gain access to the Vue instance you'll need to move this line this.$refs.container.appendChild(instance.$el) somewhere inside the default export, for example in the mounted hook or inside one of your methods.

See this CodeSandbox for an example of how you may go about this.

Below is a simplistic solution that works (I'm not an expert in Vue 3).

The main point is to use addRoute before pushing to it, because you cannot specify the route component when pushing to a route.

Here is the codesandbox with the working solution.

 <template>
  <router-link to="/">Home</router-link>
  <button @click="createComponent">Create Component</button>

  <router-view></router-view>
</template>

<script>
import { getCurrentInstance } from "vue";
import { useRouter } from "vue-router";
export default {
  name: "App",
  setup() {
    const app = getCurrentInstance().appContext.app;
    const router = useRouter();

    const createComponent = () => {
      // Check if the component has been alreadey registered
      if (!app.component("NewComponent")) {
        app.component("NewComponent", {
          name: "NewComponent",
          template: `<div>This is a new component</div>`
        });
      }

      const newComponent = app.component("NewComponent");
      // Adding a new route to the new component
      router.addRoute({ path: "/new", component: newComponent });

      router.push("/new");
    };
    return {
      createComponent,
    };
  },
};
</script>