the subject has been faced many years ago an super well applied in EU privacy regulations: Google knows it very well, and in super details and I have no doubt they will be fined for this despite all reduction of it thanks to their lobbying (and corruptions, too, in my super personal opinion): this fact well explain EU fines based on company's income.
why would they be fined for this? In fact a local LLM is exactly the opposite direction of a privacy concern. The local LLM gives an answer generated locally and never uploaded to a server.