How it checks
hourly and on wake it runs brew outdated --json=v2, which reads what Homebrew already knows. Update Homebrew runs brew update to fetch the latest first.

About
What Homebrew can upgrade, in the menu bar. The number is how many formulae and casks are outdated; the panel lists them with Upgrade on each row and Upgrade All at the bottom.
Inside
hourly and on wake it runs brew outdated --json=v2, which reads what Homebrew already knows. Update Homebrew runs brew update to fetch the latest first.
show casks, hide pinned formulae, include casks that update themselves (--greedy), and a notification when new updates appear.
Upgrade All Homebrew Packages, Update Homebrew, Outdated Homebrew Packages.
outdated lists what can be upgraded.
Install
Don't have Stackbar yet? Download it free.
stackbarctl install --index https://navbytes.github.io/stackbar-plugins/index.json io.navbytes.stackbar.plugins.homebrew