Looking at Chrome DevTools Network panel for the demo, it appears it has to do with a CORS problem:
Cross-Origin Resource Sharing error: MissingAllowOriginHeader
Looking through other Netlify Support Forums posts, there is another post from Mar 2021 by @derek-zhou suggesting that static sites should be made more liberal with CORS, as other hosting platforms have done:
@clarnx would you have an update from Netlify’s teams on the Mar 2021 request?