I asked both DeepSeek and ChatGPT what thd do with the data they collect about me. DeepSeek pointed me to reading their docs. I looked at the docs and their FAQs but couldn't find anything relevant to my question. ChatGpt was forthright about it with this answer:
"I use the information I remember about you to make our conversations more relevant and helpful. For example, I recall that you're developing a browser extension and a prompt engineering workshop, so I can tailor my responses to those topics without you having to repeat yourself.

I don’t share your data with anyone, and you can ask me to forget things whenever you want. Let me know if you’d like me to update or remove anything!"