## System details

- Omarchy: `4.0.1-1`
- Brave Origin Beta: `brave-origin-beta-bin 1.94.112-1`
- CPU: AMD Ryzen 7 250 with Radeon 780M Graphics
- GPUs: AMD HawkPoint1 and NVIDIA GeForce RTX 5060 Max-Q / Mobile

## Description

Omarchy theme changes are not applied to Brave Origin Beta. With the Catppuccin theme active, Brave Origin Beta remains in the light theme even though GNOME's color scheme is `prefer-dark` and Omarchy generates the expected Chromium color (`30,30,46` / `#1e1e2e`).

The installed browser runs from:

```text
/opt/brave.com/brave-origin-beta/brave
```

and is launched with:

```text
/usr/bin/brave-origin-beta
```

## Steps to reproduce

1. Install `brave-origin-beta-bin`.
2. Launch Brave Origin Beta.
3. Apply a dark Omarchy theme, for example `omarchy theme set catppuccin`.
4. Observe that Brave Origin Beta remains light.

## Expected behavior

Brave Origin Beta should receive the same `BrowserThemeColor` and device color-scheme policy as the other Chromium-family browsers and refresh when an Omarchy theme changes.

## Cause

`omarchy-theme-set-browser` currently writes Brave policy only through:

```bash
set_browser_policy /etc/brave/policies/managed
```

but `set_browser_policy` returns when the directory does not already exist. The `brave-origin-beta-bin` installation does not create `/etc/brave`, so no Brave policy is written.

The live-refresh logic also only covers stable Brave and the older Brave Origin layout:

```bash
refresh_running_browser brave brave
refresh_running_browser /opt/brave-origin-bin/ brave-origin -f
```

It does not match `/opt/brave.com/brave-origin-beta/` or invoke `brave-origin-beta`.

## Confirmed workaround

Creating Brave's managed-policy path as a link to Omarchy's existing Chromium policy directory allows Brave Origin Beta to consume the generated theme policy:

```bash
sudo mkdir -p /etc/brave/policies
sudo ln -s /etc/chromium/policies/managed /etc/brave/policies/managed
omarchy theme set catppuccin
brave-origin-beta --refresh-platform-policy --no-startup-window
```

Afterward, `brave://policy` should show:

```text
BrowserThemeColor  #1e1e2e
BrowserColorScheme device
```

## Suggested fix

1. Ensure `/etc/brave/policies/managed` exists during Omarchy installation/setup, or deliberately share the Chromium managed-policy directory with Brave.
2. Extend `omarchy-theme-set-browser` to detect the Brave Origin stable/beta/nightly/development executable names and their current `/opt/brave.com/...` process paths.
3. Refresh each running detected channel with its corresponding command, including `brave-origin-beta`.