From the docs you can can see that if you doesn't provide data-login_uri attribute, google will redirect to same page where you clicked the login button, if you are planing to post the credintial JWT after login to http://localhost:3000/oauth then the html must be like this

      <div
        id="g_id_onload"
        :data-client_id="googleClientId"
        data-ux_mode="redirect"
        data-auto_prompt="false"
        data-login_uri="http://localhost:3000/oauth"
        :data-callback="getGoogleLoginCallback"
        style="z-index: 100000000000000000"
      ></div>
      <div class="g_id_signin"></div>

I am not recommending this way of using html in your Vue app, this may not work if the component containing this html is mounted after the library is loaded

Instead Use renderButton function

Instead you can use google.accounts.id.renderButton function to dynamically create a Login Button.

Or Use a Plugin Instead

You can easily do the same using this Vue 3 plugin vue3-google-login which I recently created for easily integrating Login With Google feature in your Vue 3 application, all you need to do is initialise the plugin in main.js with your client id then use the component GoogleLogin like this

<script setup>
const idConfiguration = {
      login_uri:'http://localhost:3000/oauth',
      ux_mode:'redirect'
    }
</script>

<template>
    <GoogleLogin 
    :idConfiguration="idConfiguration"
    />
</template>