A number of websites are starting to require an email in the user-agent header, as a way to identify your traffic specifically. This is in many cases done to be able to better identify scrapers and either apply rate-limits or contact the owner and ask them to cool down. (Generic browser user-agents will obviously be exempted from providing an email address).
The weird part doesn't seem to be that Claude Code would add an email address to a user-agent header, actually as a site operator that feels like a nice thing to do. The weird part is sites harvesting the emails and sending them spam.
Claude Code is actually doing, perhaps not the right thing, but it is being slightly more respectful towards website operators, in letting them know who is responsible for the agent traffic.