The docs for Jira Cloud are a bit contradictory about whether an addon can store properties against a user.
This page says it’s possible, yet links to the Cloud API reference which says addons don’t have access to the user property endpoints.
The page was last updated in August 2017, and the API reference page doesn’t seem to have a last updated date on it.
I’m even having trouble using
/rest/api/2/user/properties outside of the addon. I’ve explicitly added properties to my user and I get an empty array back for the keys.