A few things...
With the axios call, try querying the relative and not the absolute url. Also, take note of the trailing slash on the url, sometimes that can trip you up depending on your template settings. Finally, you probably don't need to set the entire response to your Vue data object, with axios you are looking for response.data.
axios.get('/ajax-actions/test-api/).then(response => (this.info = response.data));
If you need to keep the full absolute url, or if you are calling the api page from a different url, then look into CORS. Setting the header below on your template should be enough, depends on your setup (eg see this topic for issues with CORS when using procache).
<php
header('Content-Type: application/json,charset=utf-8');
header("access-control-allow-origin: *");
//...
?>