Yes, local for anything that can run locally. For higher-end model needs there are privacy platforms like Venice (https://venice.ai/privacy) with ZDR legal contracts and multiple E2EE options for their open-weight models. The OpenAI/Anthropic/Google models are also available through through them but at least your identity is anonymized, though the contents of your prompt could still be stored by the destination company.
I might be missing something here but how does this change anything?
'No attorney-client relationship exists "or could exist, between an AI user and a platform such as Claude," Rakoff wrote'.
A local model or Venice are still platforms, just local.
Nerd smarts seldom survive real world smarts. Reminds me of this: https://xkcd.com/538/
I would not trust any anonymization service that still connects to gemini/openai/claude, they simply have too much reach to have any confidence that they can't [re-]connect a session to you via means other than the login and ip address.