Add slash command for starting a truly new session (not just /clear)

Problem

/clear (and its aliases /reset, /new) clears the conversation messages but stays in the same session. System prompts, tool schemas, MCP configs, and loaded skill definitions all persist and consume context — I've seen 48% context used immediately after /clear in VS Code with a few MCP servers and skills loaded.

There's no way to start a completely fresh 0% context session from within the conversation. In the CLI you can exit and run claude again, but in the VS Code extension the only option is the Command Palette ("Claude Code: New Conversation"), which isn't discoverable.

Proposed solution

Add a built-in slash command (e.g. /new-session) that starts a completely new session — new session ID, fresh context window, 0% usage. The current session would still be available via /resume.

This is distinct from /clear which should continue to work as it does today for when you want to reset the conversation but keep the loaded context.

Context

This is particularly useful when:

• MCP servers and skills have bloated the session context
• You've finished one task and want to start a completely unrelated one
• Context is too high to do meaningful work after /clear