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.
I was afraid this was going to be the answer :( We are currently using python scripts and I thought there has to be a better way but couldn't find any
Upon further research I found OpenHTF (https://github.com/google/openhtf) which is opensource. And, if you don't want to spin up your own dashboard, there's tofupilot (https://www.tofupilot.com/) but this is paid and not affiliated with google. Note, tofupilot maintains the documentation for OpenHTF (https://www.openhtf.org/)