Structured Data in the form of JSON-LD should be added to both Themes blocks and output types. For SEO this would both contribute to Site Authority and optimize SERP presentation.
Example JSON-LD could include the following schema.org vocabulary:
https://schema.org/NewsArticle - conditionally placed in output types for article pages.
https://schema.org/CollectionPage - for output types of homepages, section pages, tags pages.
https://schema.org/author - for author references.
https://schema.org/breadcrumb - to optimize SERP presentation.
https://schema.org/SiteNavigationElement - to encourage better understanding of site navigation and Site Link presentation for SERPs.
https://schema.org/Organization - for contextualizing the business vertical of a site.
https://schema.org/SearchAction - encourages search integration as well as SERP inline search.
Several other examples recommended by Google can be found on the Google Search Gallery:
https://developers.google.com/search/docs/guides/search-gallery
Thanks for this Eric – we understand the use case here and want to add support for this. I'll give an update on when that might be timing-wise once we know that.