Ctrl+L should preserve terminal scrollback history

Summary

When pressing Ctrl+L to clear the screen, the previous conversation output is lost and cannot be scrolled back to. I'd like Ctrl+L to behave like the terminal clear command — the screen clears and the prompt moves to the top, but you can still scroll up to see previous output.

Current behavior

• Ctrl+L clears the screen and conversation output is gone from scrollback
• No way to scroll back up to see previous conversation
• /clear resets the entire conversation context

Desired behavior

• Clearing the screen should preserve scrollback history, so you can scroll up to review earlier conversation output
• The prompt should appear at the top of the terminal after clearing, similar to how the clear command works in a normal terminal

Motivation

After a long conversation, the prompt sits at the bottom of the terminal. I prefer working with the prompt near the top of the screen. The terminal clear command solves this perfectly in normal shell usage — it'd be great to have the same behavior in Claude Code.