Add "clear display" action that clears terminal output without resetting conversation context

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

In long Claude Code sessions, the terminal accumulates a lot of output — tool calls, diffs, responses — making it visually noisy and hard to navigate. There's no way to wipe the visible output without also losing the conversation context.

/clear resets the screen but also clears context, which destroys the session state. The current ctrl+l binding (app:redraw) refreshes the display but doesn't clear it. There is no action that does what ctrl+l does in a normal terminal: clear the visible output while preserving history and state.

Proposed Solution

Add a new keybinding action app:clearDisplay (or similar) that clears the visible terminal output without touching the conversation context. Bind it to ctrl+l by default (replacing or supplementing app:redraw), matching standard terminal behavior.

Alternative Solutions

Currently using /compact as a workaround, but that alters context. Opening a new session loses all history. Neither is a real substitute for a simple visual clear.

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

1. I've been working in a session for 30+ minutes with many tool calls and diffs
2. I want a clean view to focus on the next task
3. I press ctrl+l — the screen clears visually, like in any terminal
4. Claude still has full context of everything we've discussed

Additional Context

Standard terminals (bash, zsh) treat ctrl+l as "clear display, preserve history." Claude Code's ctrl+l (app:redraw) doesn't match this expectation. The fix is purely a new action in the keybinding system — no context or model changes required.