Given chatgpt is a security risk and even in a controlled closed environment data used to train AI requires security, not to mention the GDPR aspects of customer data.. it’s likely to be quite a while before we see data processed by AI.
Customer data is already processed by AI and has been for many years now.
If you have a Gmail account you'll see there's a spam filter, if you have a netflix account you'll see that they recommend movies and TV shows based on what you've already watched, if you have social media accounts they'll target ads to you.
Chatgpt isn't the only LLM in existence, not all of them require accessing a third-party service via an API as already pointed out.