The link to the latest version of the Data360 Analyze REST API documentation is available in the System administration > API developer documentation topic of the online Help documentation.
The latest version is currently Data360Analyze Version 382.8.4, 2021-11-29 which is newer than the version you referenced.
There are no published APIs for managing Run Property Sets. As you note, a Run Property Set can be created, replaced or exported using the AnalyzeCli tool - this is currently the only means of managing them other than via the UI.
Regards,
Adrian