feat: Add env var for custom Chromium browser path

Problem

The /chrome feature only detects Google Chrome. Users with alternative Chromium-based browsers can't use browser control even with the Claude extension installed and working.

Use Case

I use Helium (lightweight Chromium browser) as my daily driver. The Claude extension works perfectly there. Claude Code just doesn't detect it.

This affects users of Arc, Brave, Vivaldi, Edge, Chromium, and other Chromium-based browsers.

Proposal

Add CLAUDE_CODE_CHROME_PATH env var to specify a custom Chromium browser path.

Configuration via settings.json:

{
  "env": {
    "CLAUDE_CODE_CHROME_PATH": "/Applications/Helium.app/Contents/MacOS/Helium"
  }
}

Or via shell:

export CLAUDE_CODE_CHROME_PATH="/Applications/Helium.app/Contents/MacOS/Helium"

Implementation

1. Check CLAUDE_CODE_CHROME_PATH first
2. Fall back to current Chrome detection if unset

This follows the existing pattern of other Claude Code env vars like CLAUDE_CODE_SHELL and CLAUDE_CODE_TMPDIR.

Related Issues

This would address multiple open issues:

• #14370 - Detect Claude Chrome extension in other Chromium-based browsers
• #14391 - Native messaging host not installed for Chromium/Brave (Linux)
• #14536 - Allow browser selection instead of opening default browser
• #14616 - Chrome integration doesn't detect extension in Brave (macOS)
• #14981 - Add browser selection option for Chrome extension (support non-default browsers)
• #17337 - Arc browser incompatibility (macOS)
• #17866 - Add --chrome-path flag to specify custom Chrome browser location