How can objects be restored in issues after the Asset catalog is deleted and backed up?
If you are using Asset object schema in issues using assets custom fields and accidentally delete the entire object schema or specific object type, as you already know there is no way to restore objects in issues with the native Jira functionality. No matter if you backed up or not the schema or object type.
The newly released version of Insight Assets Backup & Migration has a new feature where you can restore objects in issues!
With the app, it is possible to restore the entire schema, specific object types, and objects in the issues. To do so on the same instance, where the backup of the object schema was taken, after restoring the schema, follow the next steps.
In the “Synced schemas” list select the schema, which has been restored and click the “Restore” button.
In the “Restores“ list click the button “Restore objects in issues“ under Actions:
In the popup you will see the list of the custom fields, where the original schema was used:
Before restoring objects in issue fields, go to the Field configuration by clicking the “Open configuration“ button.
Edit “Assets object/s field configuration” and enter a newly created schema instead of the original one:
When a new schema is selected, go back to Insight Assets Backup and Migration App and click the “Restore” button:
To restore the objects selected in the issues, the user account, by which the plugin is configured, should have “Edit Issue” permission!
The restore will restore the objects in the issues, which were selected at the moment of the backup!
If you want to restore on another instance or from DC/Server, you can do it as well!
Before starting the process, the following prerequisites should be fulfilled:
Make sure that the projects and issues are already migrated
Server/Data Center to Cloud
Use Atlassian-recommended methods, which preserve Jira issue keys of the Server/DC issues in the target Cloud. See more details on the following page: What is Jira Cloud Migration Assistant? | Atlassian Support
Cloud to Cloud
Use Atlassian-recommended methods, which preserve Jira issue keys of the original issues in the target Cloud. See more details on the following page: Merge multiple Jira Cloud sites | Jira | Atlassian Documentation
From the available methods, Using a CSV file to import issues will not be suitable for further restoring the objects in Jira issue fields, as in this case original issue keys are not preserved!
The user (email) indicated in the current connection must be added to the project(s) and have valid permission to view and edit the issues.
Here you can see the complete documentation for the feature.
Insight Assets Backup & Migration has the ability to migrate and restore object schema from the data center or server instance to the destination cloud instance, as well as from one cloud to another. For more details, view the article 
How can Assets be migrated from Jira Data Center to Cloud or from one Cloud to another instance?
If you have more questions or suggestions feel free to contact Twinit support.