[Feature Request] Add `/new` command to start fresh session in same terminal

Feature Description
Add /new command to start a fresh session in the same terminal tab

Feature Request

Problem

Currently there's no way to start a new Claude Code session from within an
active session. The options are:

• /clear — resets context but stays in the same session
• Exit and re-run claude — works but is clunky in the CLI
• --resume picker — for resuming old sessions, not starting fresh

Proposed Solution

Add a /new slash command that closes the current session and starts a
fresh one in the same terminal tab (equivalent to exec claude but
accessible as a first-class command).

Expected Behavior

• /new ends the current session
• A new Claude Code session starts immediately in the same terminal tab
• No context or history carried over (truly fresh session)

Environment Info

• Platform: darwin
• Terminal: ghostty
• Version: 2.1.185
• Feedback ID: b500d57d-6ecd-411b-827c-50ca9c2f4031