What I would do is clone the original clipping plane list and re-assign it to all tilesets as needed. However, since clipping planes are defined relative to the local coordinates of each object they’re attached to, you’ll need to apply an additional transform to reverse that in order to define a clipping plane in a global coordinate system that affects all tilesets in the same way (something like this: 3d-tiles & Clipping Planes).
We do have an open issue here to consider removing the ownership from clipping planes so you can just define them globally as you describe: https://github.com/CesiumGS/cesium/issues/8554