Supporting morph targets in vertex shader means the vertex stream would have to contain all morph shape vertex positions interleaved, and they need to affect the whole mesh. Currently you can't define arbitrary vertex declarations in Urho3D (ie. multiple position attributes) so it would not work without some changes to the model format, exporters, and the graphics API. I will not give any promises on this, and neither on Turso3D's capabilities. Turso3D is for now mostly a toy engine for testing things and it will develop (for example get animation features) if I have a use and interest for it, but you should certainly not count on that.
for an example of how morphing would be done with shaders. I'm somewhat skeptical of this as a scalable solution, as the vertex size and the amount of streamed data on GPU grows for each morph shape, and even more if you would also include multiple normals & tangents. For one morph shape it would likely be fine though.