[SOLVED] Site based on official Hugo documentation layout not adding baseurl to images

That’s correct behavior. Hugo will only render the value of {{ .Site.BaseURL }} where it is explicitly referenced in a template or when adding cross-references.

What you can do with your theme is to add the HTML base tag in the header section of layouts/partials/header.html (assuming you’re using that partial):

<head>
  <base href="{{ .Site.BaseURL }}">
  ...
</head>

This will make the browser implicitly prepend the base URL to every relative path in the template.