It could easily have been my fault for the comment not pushing through. I’m still working out some issues, but I’m trying my best; sometimes it’s guesswork if people are moderating contents in which case I can’t quite tell if things went through. I can manually syndicate, just to make sure; you’ll just have to excuse/delete the duplicates.
I think a lot of the things you’re talking about are often best baked directly into your theme or at worst perhaps using a plugin and/or widget if they’re easier. I know the IndieWeb Plugin has an h-card widget, but I wanted some more control, so I made my own by hand and dumped the code into the widget that appears on my homepage. I just used the typical WordPress widget system and dumped it into the sidebar area for my homepage.
As for summaries, you typically add them as sub-microformats to things like h-entry. Thus you’d want to add something like p-summary instead of the older entry-summary or e-summary. I think that some of this was being worked on in Independent Publisher already, but haven’t noticed if it’s being actively used in the current version. Often many themes will use the WordPress “Excerpt” field in the admin UI to add a summary which would have this microformat on it for use elsewhere whether it’s displayed or hidden within the page source for open graph data which is used by Twitter or Facebook. The p-summary would typically be added by the theme itself depending on where it’s used.
I could have sworn that the Independent Publisher Theme used and displayed WordPress’s built in categories and tags details for posts, so that should cover your needs there hopefully.
The syndication links on comments are a hidden bit of functionality and aren’t documented well (or at all?). I recall stumbling across the functionality myself. The syndication links plugin definitely adds the functionality, and depending on how the comment is received, it can sometimes display them automatically. Generally however, I’m often syndicating things I write in comments manually to Twitter (often using it as a notifications system for those without webmention support). Then I’ll go to the particular comment I syndicated and “edit” it, either by using the admin UI directly at
/edit-comments.php or by clicking on the “edit” button on the public facing comment on the particular page. Then scrolling down that page you’ll find the Syndication Links meta box which will allow you to manually add the link! Eventually plugins like Bridgy Publish might automate some of this better, but for now, that’s where it’s hiding.