[Feature Request] Add session management to preserve context while starting fresh conversations

Feature Request
Add the option to have start a new session with fresh context, but preserve the existing one to be able to resume it.
Right now if I want to work on something new I can do /clear, but that would erase it all forever. I asked claude about it, and I couldnt have phrased it better myself :)

Here is our conversation:

me: Isnt it odd you dont have the option to do that in the product? is there a reason why you would prefer users not do this?

⏺ Honestly, yeah, it does seem like a gap. A "new session" command that archives the current conversation and starts fresh in the same terminal would be the natural UX. Right now you're stuck choosing between:

• /clear — destructive, loses everything
• /compact — not a clean break, carries summarized baggage
• Exit + restart — works, but clunky

There's no good reason a user shouldn't be able to just say "start fresh" without losing history or leaving their terminal. It's the equivalent of "new tab" in a browser.

Environment Info

• Platform: darwin
• Terminal: iTerm.app
• Version: 2.1.50
• Feedback ID: de15ed86-2461-4a85-a43a-1bcf965762f9