feat(cli): detach tray mode from terminal (#11230)

Validated on the combined batch board over tip 0b41259f: static gates clean, typecheck:core clean, 430+ focused tests green across 5 groups.

--tray returns after readiness and survives terminal close, with tray-mode autostart on macOS/Windows/Linux while headless Linux keeps the systemd user service. tray-detached + autostart suites green. Closes #11229. Thank you @tuandinh0801!

docs/guides/USER_GUIDE.md

@@ -357,6 +357,49 @@ omniroute --port 3000
 
 The CLI automatically loads `.env` from `~/.omniroute/.env` or `./.env`.
 
+### Tray mode
+
+Start OmniRoute in the system tray:
+
+```bash
+omniroute serve --tray
+```
+
+The command returns after the server and tray are ready.
+
+The server continues without the terminal.
+
+Tray mode supports macOS, Windows, and graphical Linux sessions. Tray mode does not open the dashboard automatically.
+
+Use the tray menu for these actions:
+
+- Open the dashboard.
+- Open `/dashboard/logs`.
+- Change auto-start.
+- Stop OmniRoute.
+
+Do not combine `--tray` with these options:
+
+- `--daemon`
+- `--log`
+- `--no-recovery`
+
+These modes require different process ownership.
+
+Enable startup at the next machine login:
+
+```bash
+omniroute autostart enable
+```
+
+Auto-start uses tray mode on macOS, Windows, and graphical Linux sessions. Headless Linux uses the existing systemd user service.
+
+Disable startup at login:
+
+```bash
+omniroute autostart disable
+```
+
 ### Uninstalling
 
 When you no longer need OmniRoute, we provide two quick scripts for a clean removal: