[BUG] Claude Code Desktop session has incomplete PATH — misses Homebrew, bun, and other user-installed tools

Description

Claude Code Desktop sessions start with a minimal PATH that only includes system directories:

/usr/bin:/bin:/usr/sbin:/sbin:/usr/local/bin

This is missing common user-installed tool paths:

• /opt/homebrew/bin (Homebrew on Apple Silicon) — gh, node, etc.
• ~/.bun/bin (bun runtime)
• Any other paths added in ~/.zshrc or ~/.bash_profile

The Desktop app appears to not source the user's shell profile when initializing the Bash environment.

Impact

Tools like gh, bun, node, npm etc. appear as "command not found" and require manual export PATH=... workarounds in every session. This breaks:

• GitHub CLI operations (gh issue create, gh pr view)
• Package managers (bun, npm, pnpm, yarn)
• Any Homebrew-installed CLI tool

Steps to Reproduce

1. Install tools via Homebrew or bun (which add to PATH via shell profile)
2. Open Claude Code Desktop, start a session
3. Run which gh or which bun → "not found"
4. Run echo $PATH → only system paths, no Homebrew or user paths

Expected Behavior

The Bash tool should inherit the user's full PATH as configured in their shell profile (~/.zshrc, ~/.bash_profile, ~/.bashrc), same as opening a terminal.

Workaround

Manually prepend paths in each command:

export PATH="/opt/homebrew/bin:$HOME/.bun/bin:$PATH"

Environment

• Claude Code Desktop (macOS, Apple Silicon)
• Shell: bash (invoked by Bash tool)
• User shell: zsh (with Homebrew and bun paths in .zshrc)