I believe the solution you are after is the "component-metadata - shares" endpoint as documented here:
https://adobedocs.github.io/analytics-2.0-apis/#/component-metadata%20-%20shares/updateShares
https://www.adobe.io/apis/experiencecloud/analytics/docs.html#!AdobeDocs/analytics-2.0-apis/master/s...
The UI uses this api when a share is made in the ui . Referencing the requests there may aid you in your proof of concept and troubleshooting the API (please note the UI will use a slightly different endpoint than you would use and is documented in the documentation linked above):

I've never used this particular API, but it appears to be suggesting the functionality you are after. I would test it on some test segments, before starting any big project.