v3 embed in Astro getting CORS issues

[Snugug]

I'm attempting to embed v3 into an Astro project (brand new project from Astro init) with the following in a admin.astro page:

<div id="app"></div>

<script>
  import { renderStudio, defineConfig } from 'sanity';
  import { deskTool } from 'sanity/desk';

  const config = defineConfig({
    plugins: [deskTool()],
    projectId: 'snow-dog',
    dataset: 'production',
    schema: {
      types: [
        {
          type: 'document',
          name: 'post',
          title: 'Post',
          fields: [
            {
              type: 'string',
              name: 'title',
              title: 'Title',
            },
          ],
        },
      ],
    },
  });

  // This assumes that there is a <div id="app"></div> node in the HTML structure where this code is executed.
  renderStudio(document.getElementById('app'), config);
</script>

This will properly pull in Sanity, but I get Unknown network error attempting to reach snow-dog.api.sanity.io. Looking in my console, it's a CORS issue (Access to XMLHttpRequest at 'https://{project}.api.sanity.io/v2021-06-07/users/me?tag=sanity.studio.users.get-current' from origin 'http://localhost:3333' has been blocked by CORS policy: No 'Access-Control-Allow-Origin' header is present on the requested resource.)

I've got CORS set up correctly in my project (see below)

Is there something else that needs to be done to get this to work?