Jira provides the ability to set custom user properties via the following :

https://<site>.atlassian.net/secure/admin/user/EditUserProperties.jspa?name=<user>

Document Reference : https://confluence.atlassian.com/cloud/edit-user-project-roles-jira-applications-only-744721647.html

At the moment, it is not possible to update the user properties via REST APIs in Jira cloud.

Suggestion :
Option 1 : Provide an option to update the current User properties via API
Option 2 : Allow custom properties for Atlassian Account to support custom properties that can be used by Jira.

Additional suggestion:
1. Migrate legacy user properties to user entities.
2. Provide UI to update user entities.
3. Update custom fields of "User property" type to reference user entity.