## What happened

`omarchy update` hung indefinitely in the first pending migration (`1787515927`, "Stop world-writable Chromium and Firefox policy directories"). The migration calls `omarchy-theme-set-browser`, which spawned a brand-new, windowless `/opt/brave-bin/brave --refresh-platform-policy --no-startup-window` process and then waited on it forever (10+ minutes until I killed it by hand). Killing that process let the migration and the rest of the update continue normally.

The same code path runs on every `omarchy theme set`, so theme changes hang the same way on this setup.

## Cause

In `bin/omarchy-theme-set-browser` (still the same on `quattro`):

```bash
refresh_running_browser brave brave
# Match on the binary path: the running process is named plain "brave", and a
# bare -f brave-origin pattern would also match the installer's own terminal.
refresh_running_browser /opt/brave-origin-bin/ brave-origin -f
```

The plain-Brave line detects a running browser with `pgrep -x brave`. As the comment on the next line already notes, the Brave Origin process is *also* named plain `brave`:

```
$ pgrep -x brave | head -1
22262
$ readlink /proc/22262/exe
/opt/brave-origin-bin/brave
$ pgrep -f '^/opt/brave-bin/brave' ; echo $?
1
```

So on a machine where both `brave-bin` and `brave-origin-bin` are installed and only Brave Origin is running, the script decides plain Brave is running and executes `brave --refresh-platform-policy --no-startup-window`. Because there is no plain-Brave instance to hand the flag to, that command starts a fresh browser process with no window, which never exits, and the script blocks on it in the foreground.

Setups with both packages seem likely to be common for a while: anyone who had `brave-bin` from an older Omarchy and then got Brave Origin as the new default browser.

## Suggested fix

Match plain Brave by binary path the same way the Brave Origin line does, e.g.

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

Independently of that, it may be worth running the refresh command in the background or under a `timeout`, so a mis-detection can never stall a migration or a theme change.

## Steps to reproduce

1. Install both `brave-bin` and `brave-origin-bin`.
2. Have Brave Origin running, plain Brave not running.
3. Run `omarchy theme set <any theme>` (or `omarchy update` with migration `1787515927` still pending).
4. Observe it never returns; `ps --forest` shows `omarchy-theme-set-browser` waiting on a `/opt/brave-bin/brave --refresh-platform-policy --no-startup-window` child with no window.

## System

- Omarchy 4.0.2-2 (aarch64 build from omarchy-mac/omarchy-pkgs-aarch64)
- Apple MacBook Pro (16-inch, M1 Max, 2021), Asahi / Arch Linux ARM, kernel 7.1.6-1-1-ARCH
- brave-bin 1:1.94.121-1, brave-origin-bin 1:1.94.121-1

The bug is platform-independent; nothing in the affected code depends on the architecture.