You're right that the thread feature itself doesn't provide any information about its location in space. However, it looks like there are a couple of relatively easy solutions.
The first is to get the original cylinders that were used as input to create the thread. However, those cylinders aren't available after the thread has been created because they may have been consumed. However, you can roll the timeline back to just before the thread feature was created and then query for the cylinders using the inputCylindricalFace property of the ThreadFeature. Then you'll need to move the timeline back to where it was.
The second is to look for a cylinder that was created as a result of adding the thread feature. I checked and it looks like even when you model the threads that all thread types will create a cylinder as part of the geometry to model the thread. I like this approach better because it's strictly a query operation and doesn't involve making changes to the model. To do this you will use the faces property of the ThreadFeature and then use the geometry property of each face and look for the face whose geometry is a Cylinder type of object. Then you can use properties on the cylinder to find the position and axis, which will be the same for the thread.
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Brian EkinsInventor and Fusion 360 API Expert
Website/Blog:
https://EkinsSolutions.com