## Description

The emoji picker (`omarchy menu emoji`, class `github` window `GitHub Copilot`) fails to insert the selected emoji into **GitHub Copilot Desktop** (an Electron/Ozone-Wayland app). Manually pasting immediately afterward also fails, because nothing remains on the clipboard.

## Root cause

`/usr/share/omarchy/bin/omarchy-menu-emoji-insert` copies the emoji to the clipboard via a short-lived `wl-copy --foreground` process, waits ~0.35s total, sends `Shift+Insert` via `wtype`, then kills the `wl-copy` process:

```bash
printf '%s' "$emoji" | wl-copy --type text/plain --sensitive --foreground &
copy_pid=$!
sleep 0.15
wtype -M shift -k Insert -m shift 2>/dev/null || true
sleep 0.2
kill "$copy_pid" 2>/dev/null || true
```

I confirmed with a manual test that `wl-copy --foreground` / `wl-paste` round-trip correctly at the compositor level (Hyprland), so the clipboard mechanism itself is sound. The problem is:

1. After the emoji picker's exclusive-focus Wayland layer closes, focus needs to return to the previously focused window before the `wtype` keystroke can land. For Electron/Ozone-Wayland apps this focus restoration appears to take longer than the ~150ms the script allows.
2. `wtype`'s synthetic `zwp_virtual_keyboard_manager_v1` events do not appear to be reliably delivered to/consumed by Electron's Wayland input backend the way they are for native GTK/Qt (Quickshell) surfaces.
3. Because the script unconditionally kills the `wl-copy` process ~350ms after starting, the clipboard entry is destroyed almost immediately — even if the automatic paste failed, there's no time window left for the user to manually press Ctrl+V as a fallback.

## Steps to Reproduce

1. Focus a GitHub Copilot Desktop window.
2. Run `omarchy menu emoji` (or trigger the emoji picker keybinding).
3. Select any emoji.
4. Observe: no emoji is typed into the Copilot Desktop input field.
5. Try manually pasting (Ctrl+V) immediately after — clipboard is already empty/reverted.

## Expected Behavior

The emoji should be inserted into the focused Electron/Copilot Desktop input field, or at minimum remain on the clipboard long enough (or indefinitely, e.g. via `wl-copy`'s normal persistent behavior) for the user to paste it manually if the automatic `wtype` paste doesn't land.

## System Details

- Omarchy version: 4.0.4-1
- wl-clipboard: 2.3.0
- wtype: 0.4-2
- Compositor: Hyprland
- Affected app: GitHub Copilot Desktop (Wayland-native Electron app, not XWayland — confirmed via `hyprctl clients -j`)
- Debug log: /tmp/omarchy-debug.log (generated via `omarchy-debug --no-sudo --print`)

## Suggested Fix

Consider reusing the more robust logic already present in `omarchy clipboard paste text --shift-insert` (which appears to be the general-purpose clipboard-paste command) instead of the emoji-specific script's fixed short timers, or increase the kill delay / make it conditional so the clipboard entry survives long enough for a manual paste fallback.