The Claude Code privacy policy[0] is pretty explicit that by default they train on neither the prompts, usage data, or even explicitly provided feedback data (presumably /bug?) that can be used for other product improvements.
> By default, Anthropic does not train generative models using code or prompts that are sent to Claude Code.
> We aim to be fully transparent about how we use your data. We may use feedback to improve our products and services, but we will not train generative models using your feedback from Claude Code.
[...]
> If you choose to send us feedback about Claude Code, such as transcripts of your usage, Anthropic may use that feedback to debug related issues and improve Claude Code’s functionality (e.g., to reduce the risk of similar bugs occurring in the future). We will not train generative models using this feedback. Given their potentially sensitive nature, we store user feedback transcripts for only 30 days.
For understanding what value they place on that data, they do have a program where you can opt-in to have your data be used for training[1] in exchange for a discount on the API rates.
[0] https://docs.anthropic.com/en/docs/claude-code/data-usage
[1] https://support.anthropic.com/en/articles/11174108-about-the...