refactor(lib): extract tray state types into own module

Move tray-related state holders out of lib.rs into a new
src-tauri/src/tray_runtime.rs:
- TrayState / TrayTooltip type aliases
- TrayPlaybackState newtype
- TrayMenuItems / TrayMenuItemsState
- TrayMenuLabels (+ Default impl) / TrayMenuLabelsState
- tray_state_icon helper

The actual tray builder + Tauri commands (try_build_tray_icon,
set_tray_tooltip, set_tray_menu_labels, toggle_tray_icon) already
lived in lib_commands/sync/tray.rs and continue to reach the types
through the existing super::* re-export chain.

lib.rs goes from 549 → 486 LOC. Behaviour-preserving — same managed
state, same Tauri State<T> registrations in run().

src-tauri/src/tray_runtime.rs

@@ -0,0 +1,68 @@
+use std::sync::Mutex;
+
+use tauri::tray::TrayIcon;
+
+/// Holds the live system-tray icon handle. `None` means the tray is currently hidden/removed.
+/// Dropping the inner `TrayIcon` fully removes it from the OS notification area on all platforms.
+pub(crate) type TrayState = Mutex<Option<TrayIcon>>;
+
+/// Cached tray tooltip text. Updated by `set_tray_tooltip` and re-applied when the
+/// icon is rebuilt (e.g. after the user toggles the tray off and on again).
+/// Empty string means "use the default `Psysonic` tooltip".
+pub(crate) type TrayTooltip = Mutex<String>;
+
+#[derive(Default)]
+pub(crate) struct TrayPlaybackState(pub(crate) Mutex<String>);
+
+pub(crate) fn tray_state_icon(state: &str) -> &'static str {
+    match state {
+        "play" => "▶",
+        "pause" => "⏸",
+        _ => "⏹",
+    }
+}
+
+/// Handles to all updatable tray menu items, kept around so `set_tray_menu_labels`
+/// (i18n refresh) and `set_tray_tooltip` (track change) can re-text them without
+/// rebuilding the whole tray icon. The `now_playing` slot is `Some` on Linux
+/// only — it surfaces the current track as a disabled menu entry because
+/// AppIndicator has no hover tooltip API.
+pub(crate) struct TrayMenuItems {
+    pub(crate) play_pause: tauri::menu::MenuItem<tauri::Wry>,
+    pub(crate) next: tauri::menu::MenuItem<tauri::Wry>,
+    pub(crate) previous: tauri::menu::MenuItem<tauri::Wry>,
+    pub(crate) show_hide: tauri::menu::MenuItem<tauri::Wry>,
+    pub(crate) quit: tauri::menu::MenuItem<tauri::Wry>,
+    #[cfg_attr(not(target_os = "linux"), allow(dead_code))]
+    pub(crate) now_playing: Option<tauri::menu::MenuItem<tauri::Wry>>,
+}
+
+pub(crate) type TrayMenuItemsState = Mutex<Option<TrayMenuItems>>;
+
+/// Cached translations for the tray menu. Defaults to English so the menu has
+/// readable labels before the frontend has had a chance to run `set_tray_menu_labels`.
+#[derive(Clone)]
+pub(crate) struct TrayMenuLabels {
+    pub(crate) play_pause: String,
+    pub(crate) next: String,
+    pub(crate) previous: String,
+    pub(crate) show_hide: String,
+    pub(crate) quit: String,
+    #[cfg_attr(not(target_os = "linux"), allow(dead_code))]
+    pub(crate) nothing_playing: String,
+}
+
+impl Default for TrayMenuLabels {
+    fn default() -> Self {
+        Self {
+            play_pause: "Play / Pause".into(),
+            next: "Next Track".into(),
+            previous: "Previous Track".into(),
+            show_hide: "Show / Hide".into(),
+            quit: "Exit Psysonic".into(),
+            nothing_playing: "Nothing playing".into(),
+        }
+    }
+}
+
+pub(crate) type TrayMenuLabelsState = Mutex<TrayMenuLabels>;