[FEATURE] Add option to disable welcome splash screen on startup

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

Feature Request

Add a setting to disable the welcome splash/banner screen that
displays on every session start.

## Current Behavior

Every time I run claude in the terminal, a welcome screen is
displayed showing:

• "Welcome back [username]!"
• Claude logo
• Model name (e.g., "Opus 4.5")
• Subscription tier (e.g., "Claude Max")
• Working directory path

## Desired Behavior

A setting like showWelcomeBanner: false or skipSplash: true in
~/.claude/settings.json to skip this screen and go directly to
the prompt.

## Use Case

For users who run Claude Code frequently, the splash screen adds
unnecessary delay and visual noise. A quick, minimal startup would
improve the workflow.

## Suggested Implementation

Add a new setting such as:
```json
{
"showWelcomeBanner": false
}

Or an environment variable:
CLAUDE_CODE_SKIP_WELCOME=1

Proposed Solution

Suggested Implementation

Add a new setting such as:
```json
{
"showWelcomeBanner": false
}

Or an environment variable:
CLAUDE_CODE_SKIP_WELCOME=1

Alternative Solutions

Or an environment variable:
CLAUDE_CODE_SKIP_WELCOME=1

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_