My team really likes the simplicity of the "Agility" templates in Jira, sometimes called "next-gen" templates.
Through the Jira integrations, we are able to sync almost everything that we need, except for the relationships using the "Linked to" field mapping.
After speaking with customer support (hi @Shawn!) and reading some of the documentation, it appears that is due to the inability to "edit" screens in Jira: https://community.atlassian.com/t5/Jira-questions/Create-add-and-edit-screens-in-Agile-board/qaq-p/913674
Perhaps there is a technical limitation on Jira's side, but it does look like this is the direction they are headed so I think it would be good for Aha! to research the feasibility.
The Aha! + Jira integration now supports Jira next-gen projects. Create a new Jira integration and follow the steps to set it up. When a next-gen project is selected, the integration will see that this is the case and add the default mappings accordingly.
This article provides more detail on how to setup a new Jira integration.