### What happened

An app with a system-tray icon (StatusNotifierItem) was already running when
omarchy-shell restarted (in my case, triggered by an IPC request — I see
`omarchy-shell[1135]: INFO: Exiting due to IPC request.` in the journal,
likely from a theme/plugin reload). After the new shell process came up, the
app's tray icon never appeared again in the `omarchy.tray` drawer, even
though the app kept running normally in the background.

I confirmed the mechanism directly over D-Bus: the app still owned its
StatusNotifierItem service name, but the new watcher's registered-item list
was empty:

    $ busctl --user get-property org.kde.StatusNotifierWatcher \
        /StatusNotifierWatcher org.kde.StatusNotifierWatcher \
        RegisteredStatusNotifierItems
    as 0

Killing and relaunching the affected app made it re-register and its icon
reappeared immediately:

    $ busctl --user get-property org.kde.StatusNotifierWatcher \
        /StatusNotifierWatcher org.kde.StatusNotifierWatcher \
        RegisteredStatusNotifierItems
    as 1 "org.kde.StatusNotifierItem-<app>-<pid>/StatusNotifierItem"

### Why

The StatusNotifierItem protocol only has clients call
`RegisterStatusNotifierItem` once, at their own startup. It has no mechanism
for a client to notice the watcher itself was replaced and re-register on
its own. So any time omarchy-shell's StatusNotifierWatcher restarts while a
tray app is already running, that app's icon is silently dropped until the
app itself is restarted — the shell has no way to know it's missing an icon
it should have.

### Expected

The tray watcher could proactively recover already-running items after its
own restart — e.g. by enumerating current D-Bus names matching
`org.kde.StatusNotifierItem-*` (or `org.freedesktop.StatusNotifierItem-*`)
on startup and querying them directly, rather than relying solely on them
calling `RegisterStatusNotifierItem` again.

### Steps to reproduce

1. Launch any app that registers a tray icon (I used ProtonVPN's GTK app,
   `proton-vpn-gtk-app`).
2. Confirm its icon shows in the `omarchy.tray` drawer.
3. Restart omarchy-shell (e.g. `omarchy-shell shell rescanPlugins`, a theme
   switch, or any other action that sends the shell an IPC restart request)
   without closing the app.
4. Hover the tray drawer again — the icon is gone. The app is still running
   and its VPN/whatever functionality is unaffected; only the tray
   registration is lost.

### System

- omarchy 4.0.3-1
- quickshell 0.3.1-1
- Hyprland, Arch Linux

### Related

Possibly the same underlying StatusNotifierWatcher-lifecycle-across-restart
root cause as #7957 ("Restarting Omarchy Shell reopens tray-resident
Spotify and steals focus"), but the opposite symptom: there, Spotify's item
survives the restart and the shell re-focuses its window; here, the item is
dropped entirely and needs the app itself relaunched to reappear.