[FEATURE] /new slash command to switch to a fresh session while preserving the current one

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Starting a new session requires exiting (/exit) and re-running claude — a minor but frequent friction. /clear clears history but doesn't create a new session, so you can't
return to the previous context via /resume. There's no way to quickly switch to a fresh session while keeping the current one alive.

Proposed Solution

Add a /new command that preserves the current session (keeps it resumable), opens a fresh new session in-place, and allows users to /resume back to the previous session
later.

Alternative Solutions

Current workaround: /exit, then run claude, then claude --resume to return. This works but adds unnecessary friction when context-switching frequently.

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

1. I'm deep in a debugging session with significant context built up
2. I need to quickly look something up or work on a different feature
3. With /new, I switch to a fresh session, do the quick task
4. Then /resume back to my debugging session with all context intact
5. Similar to opening a new browser tab while keeping the old one

Additional Context

_No response_