Currently, there is no option to update Insight Object Attribute value using JSM Automation (or) Jira Automation. Having an option to update the Insight Object attribute in JSM (or) Jira Automation will be more useful while trying to update Insight Object Attribute based on events associated with Jira changes.

This is already possible on Cloud version of Automation for Jira.

https://confluence.atlassian.com/jirakb/how-to-update-asset-object-attribute-using-automation-with-values-from-associated-jira-issue-1085200114.html

This feature request remains to add the same or similar feature to Data Center.