### System details

ThinkPad T14s Gen 6; Intel Core Ultra 5 228V / Intel Arc 130V/140V; Omarchy 4.0.0-1; Hyprland 0.56.2.

### What's wrong?

After upgrading from Omarchy 3 to Quattro, the Apps menu contained broken icons for surviving custom launchers and a dead Alacritty launcher with a generic icon.

The pre-upgrade launchers included:

```ini
# GitHub.desktop
Icon=$HOME/.local/share/applications/icons/GitHub.png

# windows-vm.desktop
Icon=$HOME/.local/share/applications/icons/windows.png
```

(Those paths are shown with `$HOME` here for privacy; the actual desktop entries contain an absolute home path.)

The Quattro upgrade moves both files out of the live icon directory:

```bash
legacy_icons_dir="$HOME/.local/share/applications/icons"
legacy_icons_backup="$HOME/.local/share/applications/icons.omarchy-upgrade-to-quattro.$BACKUP_SUFFIX.bak"
# ...
mv -f "$legacy_icons_dir/$icon" "$legacy_icons_backup/"
```

The custom `.desktop` files survive, so their absolute `Icon=` references become dangling. The shell then repeatedly logs errors such as:

```
QML QQuickImage ... Cannot open: file://$HOME/.local/share/applications/icons/GitHub.png
QML QQuickImage ... Cannot open: file://$HOME/.local/share/applications/icons/windows.png
```

The same upgrade also creates `~/.local/share/applications/Alacritty.desktop` even when `alacritty` is not installed:

```bash
if [[ -f $root/default/alacritty/Alacritty.desktop && ! -f $HOME/.local/share/applications/Alacritty.desktop ]]; then
  cp "$root/default/alacritty/Alacritty.desktop" "$HOME/.local/share/applications/"
fi
```

On this machine, `command -v alacritty` fails and no `alacritty` package is installed, but the Quickshell Apps menu still shows this entry (despite `TryExec=alacritty`) with a generic gear icon. Selecting it cannot launch anything.

### Steps to reproduce

1. On Omarchy 3, have a surviving custom desktop entry whose `Icon=` points at one of the legacy stock PNGs under `~/.local/share/applications/icons/` (for example `GitHub.png` or `windows.png`).
2. Do not have Alacritty installed.
3. Run the Quattro upgrade.
4. Open Omarchy menu → Apps.
5. Observe missing icons for the surviving launchers and a ghost Alacritty entry.
6. Inspect `journalctl --user` for the `QQuickImage Cannot open` warnings.

### Expected behavior

- Before moving legacy icons, the migration should preserve any icon still referenced by a surviving desktop entry, or rewrite that entry to a valid hicolor icon name/path.
- `Alacritty.desktop` should only be copied when `alacritty` is available, matching `omarchy-refresh-applications`'s existing command check.
- The post-upgrade Apps menu should contain no dead launchers or dangling icon paths.

### Verified workaround

Restoring the referenced PNGs from `icons.omarchy-upgrade-to-quattro.*.bak`, removing the Alacritty desktop entry when its executable is absent, running `update-desktop-database`, and refreshing the Omarchy menu fixes the problem. A follow-up scan found no unresolved absolute icon paths, and the shell produced no new icon-load warnings when the menu was reopened.