I have the Shuttle 48TB Thunderbolt 3 here. There are long running background tasks running on the Shuttle - Media Patrol and Redundancy Check. Do these require the G Speed Software Utility to be up to monitor those tasks?
No they will run without the software being actively open.
Do I need the Windows laptop to be powered on then?
Yes, the system would need to be on in order for the device to be on.