It's because Claude Code inserts a "hidden" (e.g. not visible to the user and very unexpected) info block to the system prompt that shows your email:

>The user's email address is [email protected]. Use it only to identify the user, such as for authorship, attribution, or filtering their own work. Never send it to an unrelated service, such as in a request header, URL, or payload, unless the user explicitly asks.

And Claude doesn't care about what the text says and when it uses cURL it will often "by accident" send your mail in the User-Agent. You can e.g. use a mod to remove that block: https://pastebin.com/ PkWEQCnu