Your concern is legit. Pro is a personal plan under OpenAI's consumer privacy policy: "When you use our services for individuals such as ChatGPT, Sora, or Operator, we may use your content to train our models." As for the API it goes under the business one: "By default, we do not use your business data for training our models."
Claude has the same personal-professional split. Free, pro and Max have trained by default since Anthropic's policy change in August 2025. API and team plans didn't. Choosing between one and another is also choosing a training default. The subscriptions offers the opt-out setting, Data Controls for ChatGPT and Account settings for Claude, and it's worth checking before paying.