If you truly believe that the ai companies, who have used essentially all of the worlds ip without asking for permission won’t use yours because you gave them $20 a month, I have some magic beans to sell you.
I do not know whether I'm misinterpreting this comment but:
Yes, the context from working sessions moves over the wire - claude "the model" doesn't work inside the CLI on your machine - it's an API service that the cli wraps.
Does Claude code copy your repository onto its server?