Subprocess Environment: Homebrew Bash Not Respected in PATH

Bug Description
## Bug: Claude CLI uses system bash instead of Homebrew bash despite correct PATH in user shells

### Environment

• OS: macOS 15.5 (24F74)
• Architecture: arm64 (Apple Silicon)
• Claude CLI version: 1.0.53 (Claude Code)
• System bash: GNU bash 3.2.57(1)-release at /bin/bash
• Homebrew bash: GNU bash 5.3.0(1)-release at /opt/homebrew/bin/bash

### Description
Claude CLI environment defaults to system bash (/bin/bash) instead of Homebrew bash (/opt/homebrew/bin/bash), even though PATH is correctly configured in user's default shells (zsh and
fish) to prioritize Homebrew binaries.

### Current Behavior

• Claude CLI's PATH has system directories (/usr/bin, /bin) before Homebrew directory (/opt/homebrew/bin)
• Results in outdated bash 3.2.57 being used instead of modern bash 5.3.0
• User shell configurations are not inherited by Claude CLI environment

### Expected Behavior

• Claude CLI should respect user's PATH configuration from their default shell
• Homebrew bash (5.3.0) should be used when available and configured in user's PATH
• Modern shell features should be available in Claude CLI environment

### Steps to Reproduce

1. Install bash via Homebrew: brew install bash
2. Configure PATH in .zshrc/.config/fish to prioritize /opt/homebrew/bin
3. Open Claude CLI with claude
4. Run which bash or bash --version in Claude CLI
5. Observe that /bin/bash (3.2.57) is used instead of /opt/homebrew/bin/bash (5.3.0)

### Impact

• Inconsistent behavior between user's shell and Claude CLI environment
• Claude gets confused with syntax.

### Suggested Fix
Claude CLI should either:

1. Source user's shell configuration files to inherit PATH
2. Provide a way to configure environment variables for Claude CLI sessions
3. Use the user's default shell's PATH when launching subprocesses

Environment Info

• Platform: darwin
• Terminal: ghostty
• Version: 1.0.53
• Feedback ID: 7b8fd571-1abb-4b30-8a90-8ed547a07b3c