Tor: Does Tor Browser save history or cookies?

Short answer

Tor Browser is designed not to retain browsing history after a session, and its cookies are limited to the current session. Selecting New Identity also clears private state and closes open tabs. This does not erase records held by websites, downloads you saved, bookmarks you kept, or information you disclosed while logged in. Treat those as separate privacy decisions.

Sources

Tor Project: About Tor Browser, Tor Project: Managing identities.