The geometry is valid and readable, but it turns out Batch Statistical doesn't like geometries with a Z-dimension (this constraint appears to be undocumented. In any case, it's not listed in the Input Geometry section of the docs).

(Interestingly enough, regular statistical seems to be completely fine with a Z-dimension)
After re-exporting my data without Z, I was able to successfully start the batch request.

However, the error messaging is still not particularly helpful for deciphering the issue when a user inputs a geometry with a z-dimension within Batch Statistical API.