I just came across this post. I've taken a look at it and I'm missing something. Had you configured the Astro config file to work with Astro SVG? It's an experimental feature and must be explicitly declared by adding the next object to that file:

experimental: {
  svg: true
}

If you don´t, you won't be able to work with the SVG component of Astro as it's being implemented.

You can see it at the bottom on the browser window as soon as the following page is loaded: Experimental SVG component in Astro docs