### What happened

When the XDG default browser is one Omarchy doesn't know about, **Defaults → Browser** cannot show it, cannot check it, and — if none of the seven known browsers are installed either — offers nothing to select.

On my machine `librewolf` is the default and `chromium` is the only browser from Omarchy's list that is installed. The menu renders exactly one row, "Chromium", unchecked. There is no indication that LibreWolf is in fact the default, and no way to pick it back if I switch away.

### Expected

The menu reflects the actual `xdg-settings` default, even when it is a browser outside the built-in list.

### Steps to reproduce

1. On a system with `chromium` installed, also install a browser not in Omarchy's list (`librewolf`, `vivaldi`, `waterfox`, …).
2. `xdg-settings set default-web-browser librewolf.desktop`
3. Open the Omarchy menu → Setup → Defaults → Browser.
4. Only "Chromium" is listed, unchecked. LibreWolf is absent.

### Cause

`default/omarchy/omarchy-menu.jsonc:143-149` hardcodes seven rows, each gated on `omarchy-cmd-present <browser>`, and each `checked` compares against a short name:

```
"checked":"[[ \"$(omarchy-default-browser)\" == \"chromium\" ]]"
```

`omarchy-default-browser` with no args maps seven known desktop ids to those short names, and otherwise falls through to:

```bash
*) env -u BROWSER xdg-settings get default-web-browser ;;
```

So for anything outside the list it emits a raw desktop id (`librewolf.desktop`) in a different format from the short names every `checked` compares against. No row can ever match, and no row exists for the browser anyway.

Worth noting `omarchy-launch-browser` already handles this correctly — it reads `xdg-settings` and resolves `Exec=` from the desktop file, so LibreWolf launches fine via Super+Shift+Return. It is only the menu that can't represent the state.

### Suggested fix

Have `omarchy-default-browser` accept and report arbitrary `.desktop` ids rather than a fixed list, and let the menu derive its rows from the installed `x-scheme-handler/https` handlers (`xdg-mime`/desktop-file scan) instead of a hardcoded set. That keeps `xdg-settings` as the single source of truth, consistent with the reasoning in #4340.

### System

- Omarchy 4.0.1-1
- chromium 151.0.7922.173-1, librewolf 154.0_2-1