Ideally it would be private.

Store: Customer ID, billing details, services/credit used.

Try not to store: The user's search queries, the user's prompt/response content, the user's web history (URLs, etc).

To avoid selling the llm prompt content you would need your own inference or a contract.

Sadly most just hoard the data and some will offer a model where they charge for privacy. They are all quite scammy.

Firecrawl: logs. Parallel: logs. Bright data: logs. Kagi: logs for abuse. Bocha, querit etc: logs logs logs. Cloudflare: doesn't say what they do. Exa: charge for no retention. Linkup: no retention on request. Brave: no retention on request, but actually approved it (win for brave).