Bash tool login shell doesn't source /etc/paths or ~/.zprofile

Description

The Bash tool reports itself as a login shell ([[ -o login ]] returns true, $- contains l), but the shell environment is missing:

1. System PATH entries from /etc/paths (e.g., /usr/local/bin is missing)
2. User environment from ~/.zprofile

The base PATH is only /usr/bin:/bin:/usr/sbin:/sbin, missing entries that /usr/libexec/path_helper would normally add for any login shell.

Expected behavior

A zsh login shell should run path_helper (via /etc/zprofile) and source ~/.zprofile, providing the full system and user PATH.

Actual behavior

Neither /etc/zprofile nor ~/.zprofile are sourced. Tools installed in standard locations (/usr/local/bin) and user-configured paths (nvm, custom bin directories) are unavailable without manually running source ~/.zprofile.

Repro

# In the Bash tool:
echo $PATH
# Output: /usr/bin:/bin:/usr/sbin:/sbin

[[ -o login ]] && echo "login" || echo "not login"
# Output: login

/usr/libexec/path_helper -s
# Output: PATH="/usr/local/bin:/System/Cryptexes/App/usr/bin:/usr/bin:..." (correct, but not applied)

which git-lfs node gh
# All not found

Workaround

Manually source ~/.zprofile before commands that need the full PATH.

Environment

• macOS (Darwin 25.3.0, arm64)
• zsh
• Claude Code (CLI)