I think h-feed and h-entry should be implemented manually by Hugo theme and/or site authors. Microformats add class names to a page, but someone still has to design a page. There’s way more diversity in h-feed design than RSS, Atom, or JSON-feed design because h-feeds are webpages meant for humans first, machines second. Providing built-in h-feed templates would be akin to providing a default incomplete theme.
That being said, I could imagine other microformats getting shortcodes and templates. A shortcode and/or partial for h-cite, h-card, etc. could work. I’ve made a few microformats shortcodes and could upstream simplified versions if there is sufficient interest.