This depends heavily on how you use these and how you have things configured. If you're using API vs web ui's, and the plan. Anything team or enterprise is disabled by default. Personal can be disabled.
Here's openai and anthropic,
https://help.openai.com/en/articles/5722486-how-your-data-is...
https://privacy.anthropic.com/en/articles/10023580-is-my-dat...
https://privacy.anthropic.com/en/articles/7996868-is-my-data...
and obviously, that doesn't include self-hosted models.