Add claude-status-bar

[szhu]

After making any changes to a cask, existing or new, verify:

• The submission is for a stable version or documented exception.
• brew audit --cask --online <cask> is error-free.
• brew style --fix <cask> reports no offenses.

Additionally, if adding a new cask:

• Named the cask according to the token reference.
• Checked the cask was not already refused (add your cask's name to the end of the search field).
  • PR claude-status-bar (new cask) #273903 was auto-closed for an incomplete template, not on substance.
• brew audit --cask --new <cask> worked successfully.
  • The repository was created on 2026-06-21, less than 30 days ago. Will resubmit after 2026-07-21.
• HOMEBREW_NO_INSTALL_FROM_API=1 brew install --cask <cask> worked successfully.
• brew uninstall --cask <cask> worked successfully.

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• AI was used to generate or assist with generating this PR. Please specify below how you used AI to help you, and what steps you have taken to manually verify the changes, including zap stanza paths.
  • Claude Code was used to draft the cask file. It also verified the SHA256 checksum, app bundle name, bundle ID (com.local.claudestatusbar), and minimum macOS version against the upstream build script. The zap paths were verified by installing the app and checking ~/Library/Caches, ~/Library/HTTPStorages, and ~/Library/Preferences for files matching the bundle ID.