[Feature Request] Add Ctrl+L keyboard shortcut for clearing terminal output

[kenzik]

Feature Request

Problem

Currently, users need to type the clear command to clear the Claude Code terminal output. This is less convenient than the standard Ctrl+L shortcut that works in most terminals and CLI applications.

Proposed Solution

Add support for Ctrl+L (Control+L) keyboard shortcut to clear the terminal output, similar to how it works in bash, zsh, and other terminal applications.

Current Workaround

Users currently work around this by:

• Typing clear command
• Using Ctrl+L doesn't work (as mentioned in #1341 where users manually clear with Ctrl+L)

Benefits

• Improved user experience and muscle memory consistency
• Faster terminal clearing without typing commands
• Standard terminal behavior users expect

Additional Context

This would complement the existing /clear command (mentioned in #1561) and provide a more intuitive keyboard shortcut for the same functionality.