Connecting multiple different dynamic data sources in PBI

Hi, TheScrub 

Don't know Jira, if you only discuss 8 Excel files and 1 database cube, Power BI supports the use of Gateway is published to the Service in the report to establish a connection with the local Excel or database, making it possible to schedule a refresh (automated refresh, the number of refreshes depends on the level of your credentials, up to 48 in a day). This refresh can take place up to 48 times a day)

Related links: 
Power BI Gateway | Microsoft Power BI
Use the on-premises data gateway app | Microsoft Learn
Configure scheduled refresh - Power BI | Microsoft Learn

According to my searches, to import Jira data into Power BI you must use the Rest API
REST APIs (atlassian.com)

Best Regards,
Yang
Community Support Team

If there is any post helps, then please consider Accept it as the solution  to help the other members find it more quickly.
If I misunderstand your needs or you still have problems on it, please feel free to let us know. Thanks a lot!

How to get your questions answered quickly --  How to provide sample data in the Power BI Forum