Add --no-banner flag to disable startup logo

Problem

The startup logo/banner creates UX issues on mobile terminals and small displays:

1. Redraws on screen rotation - The logo reappears every time the screen orientation changes, wasting valuable screen space
2. Reappears after /clear command - Cannot be permanently dismissed during a session
3. Takes up limited screen space - Particularly problematic on mobile SSH clients

Use Cases

• Mobile SSH clients (Termux, Blink Shell, iSH)
• tmux/screen sessions accessed from mobile devices
• Embedded terminals with limited vertical space
• Automated scripts and CI/CD pipelines

Proposed Solution

Add one or more of the following options to disable the startup banner:

• Command-line flag: claude --no-banner
• Environment variable: CLAUDE_NO_BANNER=1
• Config setting in .claude/settings.json: "ui.showBanner": false

Current Workaround

Currently using workarounds like sending multiple newlines after startup to push the banner off-screen, but this doesn't solve the /clear redraw issue.

Impact

This would significantly improve the mobile development experience and make Claude Code more accessible on resource-constrained displays.