[FEATURE] `/new` command to end current session and start a new named session

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

## Summary

Add a /new slash command that ends the current session and immediately
starts a new named session, without requiring the user to exit and
relaunch Claude Code manually.

## Motivation

When working on multiple unrelated tasks, it's useful to keep each task
in its own named session for easy retrieval via /resume.

Currently, starting a new named session requires:

1. Typing exit to leave the current session
2. Running claude -n "session name" in the terminal

This interrupts the flow, especially when switching tasks frequently.

## Related

• /resume for session management
• /clear for resetting context within a session

Proposed Solution

## Proposed behavior

/new "session name"

• Saves and closes the current session
• Immediately starts a new session with the given name
• If no name is provided, starts an unnamed new session (equivalent

to current /clear behavior, but as a fresh session)

Alternative Solutions

## Current workaround

• exit + claude -n "name" from the terminal
• Shell alias: alias cn='claude -n'

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_