This is cool conceptually, but "y" do I have to login to your site if it is local and uses my Claude Code?

y uses your local Claude Code/Codex and your local files. Your chats stay local too - I never get them. Login is for account/product features like feedback, usage analytics, and updates, not for proxying your repo or chat history through us. Details: https://ytimesy.com/privacy and https://ytimesy.com/terms