It is illegal to spend state money (i.e. wages for state and local police) to enforce federal law (the feds have their own budget for that).

California law also makes it illegal to do federal enforcement with state resources and specifically makes sharing this license plate information with federal investigators by state and local police illegal.

This has nothing to do with the supremacy of federal law over state law. It has to do with who does the enforcement of these laws. It is similarly illegal for me to enforce federal law, but I am certainly bound by it.