Stale 'Update available' banner on macOS when already on latest version (Homebrew)

Bug Description

Claude Code displays "Update available! Run: brew upgrade claude-code" at session start, but running brew upgrade claude-code confirms the latest version is already installed.

Steps to Reproduce

1. Install Claude Code via Homebrew
2. Ensure latest version is installed (brew upgrade claude-code → "already installed")
3. Start a new Claude Code session
4. Observe "Update available!" banner at the top

Expected Behavior

No update banner when already on the latest version.

Actual Behavior

Banner persists despite being on the latest version.

Environment

• OS: macOS (Darwin 25.4.0)
• Install method: Homebrew
• Claude Code version: 2.1.79
• brew upgrade output: "Warning: Not upgrading claude-code, the latest version is already installed"

Notes

Likely caused by version check comparing against npm registry rather than Homebrew's version. Related to #18047, #17825, #35586.