Publish as a Homebrew Formulea

### 🤔 What's the problem you're trying to solve?

Currently you have to download the script manually or use the `--update` command which is a bit janky. It would be nice to have an easy way to install the script.

### ✨ What's your proposed solution?

Publishing the script as a Homebrew Formulea. Get rid of the ugly update command.

### ⛏ Have you considered any alternatives or workarounds?

Don't do anything. It's just for the benefit of 3 people.

### 📚 Any additional context?

_No response_

The issue names no files or tests. Start by tracing how the script is currently downloaded and how the --update command works, then inspect the project’s release packaging. Done means the script can be installed through a Homebrew formula and the existing update workflow is no longer needed.

Written by the indexing model from the issue text.