Two possible steps:
For 1, Page info in search results mentions how Hovercards does it as an alternative.
For 2, I'm not sure how a third-party site could reuse our CSS and JS ResourceLoader modules. mw.loader.load( 'ext.popups; ) is all I need to make it go on a Wikimedia site...
Do you mean https://www.mediawiki.org/wiki/Beta_Features/Hovercards? As in something that could be used by third parties in non-MediaWiki environments?
I mention how Hovercards does it as an alternative on [https://www.mediawiki.org/wiki/API:Page_info_in_search_results#Alternatives | Page info in search results], so I'm removing this from February in favor of T88409: Showcase/inspire: Mobile page description from Wikidata.
Yes, I believe you could do something similar on a third-party web site. The intriguing part that's independent of how Hovercards makes API requests is: how much of the JS and CSS can a third-party site reuse. mw.loader.load( 'ext.popups; ) is all I need to make it go on a MW site.
The Web-APIs-Hub project is dead hence mass-declining its tasks to reflect reality. It might be superseded by a Developer Portal in the future.