Okay, that makes sense. The .iga format can be used to create display meshes as well as for isogeometric analysis. The .iga format can also be used to represent NURBS surfaces I believe. Catmull-Clark subdivision surfaces can also be represented by T-splines, although there is some approximation near star points / singularities.
However .iga is a strongly opinionated format, in that it assumes that everything can be expressed as a finite number of Bezier surface elements, where the Bezier surface control points are linear combinations of other control points. Subdivision surfaces near a star point are actually an infinite series of smaller and smaller Bezier patches, which is not representable by the .iga format. That’s also why we do approximation when we use a T-spline as a subdivision surface.
In terms of file format, there are two file formats in use by T-splines - .tsm and .tss. .tsm is a single object, and .tss contains other objects, like curves and simple nurbs surfaces. The Rhino plugin can export either of these. Neither of the formats contain enough information about T-splines to directly use for IGA, you’d need something to extract Beziers from the T-spline control mesh. That operation is not trivial, unfortunately.
As for what CAD software natively supports T-splines, Autodesk owns the T-splines library, and is including it in various of their products. It’s currently available as a native surface type in Fusion 360. Other products are going to be released that integrate it as well, but I don’t think the details are public yet.
You might also want to get in touch with Mike Scott at BYU, if you aren’t already. He’s the one that created the .iga file format.