"Update available! Run: brew upgrade claude-code" shown even when already on latest version (Homebrew cask install)

When installed via Homebrew cask (brew install claude-code), the status bar permanently shows "Update available! Run: brew upgrade claude-code" even when the latest version is already installed.

Steps to reproduce:

1. Install via brew install claude-code
2. Run brew upgrade claude-code → "Warning: Not upgrading claude-code, the latest version is already installed"
3. brew outdated shows nothing
4. Status bar still shows the update nag

Expected: No update notification when already on latest version.

Root cause (suspected): The update checker appears to compare against the npm registry version rather than the Homebrew cask version, causing a false positive for cask installs.

Environment:

• claude-code 2.1.66 (Homebrew cask)
• macOS Darwin 25.3.0