Recent Kinds Widget
It’s a reasonably frequent design/functionality pattern to see widgets from social media services. (Goodreads is an example that provides a widget for recent reads. Twitter does so for notes. There are countless others.) 
In an IndieWeb world, it would be nice to highlight what one has recently read, watched, or listened to (as examples). Towards this functionality, it would be nice if Post Kinds could provide the ability to add widgets for a variety of the post kinds to sidebars or footers.
As a baseline I could envision each widget having:

a configurable title (“Recently read”, “Food diary” for eats & drinks, “Microblog” for recent notes, bookmarks, etc.)
a chooser for one (or more) of the many various (enabled) kinds
a variable N to allow for display of the N most recent of the chosen kinds; 5 or 10 might be a reasonable default; a time-based variable to run across the post within a recent period (days, weeks, months) might be a an interesting alternative as well

For display of a single kind, the widget might default to displaying:

a heading made of the post kind icon along with “Recent [Post Kind Name plural]”
Response Property Name (wrapped with the original permalink if it exists) by Author name (if it exists)
An optional published date for the original content (if it exists) or the date the site owner published the post kind (if it exists) (the original content date would be better for context, I think)
A fleuron () or hash (#) which could be wrapped with the permalink of the original Post Kind post.

UI example: 

Recent Watches
“Cobra Kai” Take a Right
“Succession” Dundee
60 Minutes (2020-10-25)
The Hunger Games: Mockingjay – Part 2 (2015)
October 20, 2020 – PBS NewsHour (2020-10-20)

 
If the chooser in the widget allows for displaying multiple kinds at the same time, then one could have a widget for “Recent Media Consumed” or for displaying a sidebar microblog that could include Notes, bookmarks, reads, etc. (Making it similar to embedding one’s Twitter feed into a sidebar.
For encouraging outside consumption, the widget could also have a small RSS icon with a link to that Kind’s (or Kinds’) feed.
Naturally there could be some configuration for reasonable display defaults for some of the various Post Kinds./
Now archive page
Given some of the potential similarity of the widget work above, it would also be fun to have Post Kinds generate an archive page that shows by kind either the N most recent posts for each kind or all the posts within the last M days, O weeks, or P months.
This could be used to automatically generate the idea of a Now page that gives a quick overview of what a person has been up to over a relatively recent time period. A month of posts would be a good default.
One might also be able to use a solution like How to Add WordPress Widgets in Post and Page Content as a means of embedding the widgets into such a Now-type page, which could give the user the ability to pick and choose which order to place the particular kinds into based on the site owner’s discretion.