The best off-the-shelf option for this is OpenTAP. (https://opentap.io/) It may take a while to wrap your head around it, but it handles a lot of the backend plumbing for you.
From what I understand, the industry generally uses NI TestStand, ATEasy, or some in-house software probably written in VB6 20+ years ago. There’s not a ton of great software options out there for this, unfortunately.