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See FilledTorus. It seems this new primitive/region must be symmetric about the xy-plane. I found this: new features at list of changes, but I can't try it out because I will not upgrade for a while.

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Although RegionQ @ FilledTorus[] returns True, TransformedRegion[FilledTorus[], transformation] does not work (it returns FilledTorus[]).

A work-around: Use DiscretizeRegion to discretize FilledTorus object to get a MeshRegion object (dr) and apply the desired transformation to the dr:

ft = FilledTorus[{0, 0, 0}, {2/3, 1}];

trf = RotationTransform[Pi/3, {1, 1, 1}];

TransformedRegion[ft, trf]

enter image description here

dr = DiscretizeRegion[ft];

tdr = TransformedRegion[dr, trf];

Show[dr, tdr]

enter image description here

Graphics3D[{Opacity[0.5], EdgeForm[], Red, tdr, Blue, dr}] 

enter image description here

Note: GeometricTransformation works fine with FilledTorus as graphics primitive:

Graphics3D[{Opacity[0.5], EdgeForm[], Red, GeometricTransformation[ft, trf], Blue, ft}]

enter image description here

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