Add 'New Conversation' option to /resume menu

Feature Request

When working in a long Claude Code session, switching to a new topic requires Ctrl+C + restarting claude. There's no way to start a fresh conversation from within the CLI while preserving the current session for /resume.

Problem

• /clear wipes the conversation history, so /resume can't find it later
• Continuing in the same session mixes unrelated topics, polluting context
• The only clean option is Ctrl+C and restarting the process manually

Proposed Solution

Add a "New Conversation" option to the /resume menu (or as a standalone /new command) that:

1. Archives/saves the current conversation (so it's resumable later via /resume)
2. Starts a fresh conversation context within the same process

This would make topic switching seamless without losing conversation history.

Why

Power users who run Claude Code for extended periods often switch between unrelated tasks. Currently there's no clean way to context-switch without exiting the process.