I built something similar for my own personal use case where it allows any LLM to float on top of all windows and chat with it. And I do not collect such info. Your data only goes to the LLM company which you are interacting with:

https://apps.apple.com/ca/app/select-to-search-ai-assistant/...

Stay tuned, we have a plan which we are anticipating to be available in a year or less, that will not store anything on our servers.