You’d really probably need the world aligned local position. UVs are not good for projecting textures like that, because the UV unwrap might not be suitable for tileable textures, and objects can and often do have more than one set of UVs.
To get the world aligned local position, each object would need to write it’s origin point into a buffer accessable by the post process material, so it could be used as an offset against the world position. This would require a custom render pass, or highjacking/recycling an existing one (such as emissive). Depending on the other aspects of the art style, those would likely require engine modification.