Indeed, VTK.js supports only vtkImageData and vtkPolyData.
The idea behind that limitation is that unstructured grids are typically large and therefore do not make sense to be loaded with a light client.
If you need to visualize large dataset, you might want to consider a remote rendering solution (-> trame). If you still want client-side rendering, you can extract the surface of your unstructured grid for visualization in VTK.js. Alternatively, you can consider VTK.wasm.
Last but not least, adding unstructured grid support in VTK.js is doable, it’s a bit of work though.