Chats are saved in the browser you used, not on our servers.
History in the sidebar lists your past chats on this device.
Spaces let you group chats by topic, such as "Endo" or "Pharm".
To remove a chat, delete it from History. To remove them all, use Settings → Data controls → Delete all chats.
Because chats stay in the browser, they won't follow you to another device, and clearing your browser data removes them. Your profile, memories, practice record and plan do follow your account.