Hello! So am Lakshmi Manasi, a product manager on Backup and Restore. As a part of Enhanced Backup and Restore Open Beta, we have APIs also open to eligible customers. Please visit here for more details. Thanks!
Oh, I see in your post to Jira Cloud Admins you wrote:
As we approach generalavailability of the new backup and restore experience, we’ll continue to refine the API based on your feedback. Currently, access is limited to Enterprise plans, but we’re exploring broader availability as a paid offering at GA. Stay tuned for updates!
Please consider this feedback that as Premium customers we very much would be interested in paying for this.