[Feature]: Distribution via Homebrew on Linux/Linuxbrew

### Pre-flight checklist

- [x] I searched existing issues and the [Roadmap](https://github.com/AprilNEA/OpenLogi#roadmap), and this isn't already tracked.

### Problem / motivation

Some folks (like myself) use an immutable Linux distro, like Bazzite. However, no current packaging options for OpenLogi exist that works for such distros. 😢

### Proposed solution

It might be easier to package up everything OpenLogi needs via Homebrew on Linux. The distance doesn't seem great when you already have a macOS cask.

Documentation: https://docs.brew.sh/Homebrew-on-Linux

### Alternatives considered

Some solutions have been proposed already (i.e., #681 or #371), but they might not fit everybody's preference.

### Related area(s)

- [ ] GUI
- [ ] CLI
- [ ] Button actions / remapping
- [ ] DPI
- [ ] SmartShift
- [ ] Per-application profiles
- [ ] Configuration (TOML)
- [ ] Auto-update
- [x] Other

### Additional context

_No response_

Start with the repository's existing macOS cask and the Homebrew on Linux documentation linked in the issue. Determine the packaging entry points and dependencies needed for Linuxbrew support; done means OpenLogi can be distributed through Homebrew on Linux, with the required packaging configuration documented or added.

Written by the indexing model from the issue text.