feat(desktop): tray unread overlay + taskbar flash

- set_tray_unread command re-renders the tray icon with a red unread dot
  composited onto the base icon (handle + base pixels kept in managed state).
- flash_window command flashes the taskbar via request_user_attention.
- Register both commands; bump cinny submodule to 107921e0 (web wiring).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

src-tauri/src/lib.rs

@@ -272,6 +272,71 @@ fn set_badge_count(count: u32, window: tauri::Window) -> Result<(), String> {
     Ok(())
 }
 
+/// Held in managed state so the tray's unread overlay can be updated at runtime.
+/// Keeping the TrayIcon handle here also keeps the tray alive.
+struct TrayUnreadState {
+    tray: tauri::tray::TrayIcon,
+    base_rgba: Vec<u8>,
+    width: u32,
+    height: u32,
+}
+
+/// Paint a small white-ringed red "unread" dot into the bottom-right corner of
+/// an RGBA buffer, in place. Cross-platform (operates on raw pixels).
+fn draw_unread_dot(rgba: &mut [u8], width: u32, height: u32) {
+    let w = width as i32;
+    let h = height as i32;
+    if w <= 0 || h <= 0 {
+        return;
+    }
+    let r = ((w.min(h) as f32) * 0.30) as i32;
+    let ring = ((r as f32) * 0.18).max(1.0) as i32;
+    let cx = w - r - ((w as f32) * 0.06) as i32;
+    let cy = h - r - ((h as f32) * 0.06) as i32;
+    for y in (cy - r - ring).max(0)..(cy + r + ring).min(h) {
+        for x in (cx - r - ring).max(0)..(cx + r + ring).min(w) {
+            let dx = x - cx;
+            let dy = y - cy;
+            let dist2 = dx * dx + dy * dy;
+            let idx = ((y * w + x) as usize) * 4;
+            if idx + 3 >= rgba.len() {
+                continue;
+            }
+            if dist2 <= r * r {
+                rgba[idx] = 0xDD;
+                rgba[idx + 1] = 0x30;
+                rgba[idx + 2] = 0x30;
+                rgba[idx + 3] = 0xFF;
+            } else if dist2 <= (r + ring) * (r + ring) {
+                rgba[idx] = 0xFF;
+                rgba[idx + 1] = 0xFF;
+                rgba[idx + 2] = 0xFF;
+                rgba[idx + 3] = 0xFF;
+            }
+        }
+    }
+}
+
+/// Overlay (or clear) the unread dot on the tray icon.
+#[tauri::command]
+fn set_tray_unread(unread: bool, state: tauri::State<'_, TrayUnreadState>) -> Result<(), String> {
+    let mut rgba = state.base_rgba.clone();
+    if unread {
+        draw_unread_dot(&mut rgba, state.width, state.height);
+    }
+    let icon = tauri::image::Image::new_owned(rgba, state.width, state.height);
+    state.tray.set_icon(Some(icon)).map_err(|e| e.to_string())
+}
+
+/// Flash the taskbar button to draw attention (e.g. a new mention while the
+/// window is unfocused). Clears automatically once the window is focused.
+#[tauri::command]
+fn flash_window(window: tauri::Window) -> Result<(), String> {
+    window
+        .request_user_attention(Some(tauri::UserAttentionType::Informational))
+        .map_err(|e| e.to_string())
+}
+
 pub fn run() {
     let port: u16 = 44548;
     let context = tauri::generate_context!();
@@ -295,6 +360,8 @@ pub fn run() {
     builder = builder
         .invoke_handler(tauri::generate_handler![
             set_badge_count,
+            set_tray_unread,
+            flash_window,
             send_notification,
             check_for_update,
             install_update,
@@ -314,12 +381,13 @@ pub fn run() {
         .setup(move |app| {
             // --- System tray: keeps Lotus Chat running in the background so
             // notifications keep arriving after the window is closed-to-tray. ---
+            let base_icon = app.default_window_icon().cloned();
             let open_item = MenuItem::with_id(app, "open", "Open Lotus Chat", true, None::<&str>)?;
             let quit_item = MenuItem::with_id(app, "quit", "Quit Lotus Chat", true, None::<&str>)?;
             let separator = PredefinedMenuItem::separator(app)?;
             let tray_menu = Menu::with_items(app, &[&open_item, &separator, &quit_item])?;
-            let _tray = TrayIconBuilder::with_id("main-tray")
+            let tray = TrayIconBuilder::with_id("main-tray")
-                .icon(app.default_window_icon().cloned().unwrap())
+                .icon(base_icon.clone().expect("bundled window icon"))
                 .tooltip("Lotus Chat")
                 .menu(&tray_menu)
                 .show_menu_on_left_click(false)
@@ -347,6 +415,19 @@ pub fn run() {
                 })
                 .build(app)?;
 
+            // Keep the tray handle (and base icon pixels) in managed state so
+            // set_tray_unread can re-render the icon at runtime.
+            if let Some(img) = base_icon {
+                let base_rgba = img.rgba().to_vec();
+                let (width, height) = (img.width(), img.height());
+                app.manage(TrayUnreadState {
+                    tray,
+                    base_rgba,
+                    width,
+                    height,
+                });
+            }
+
             #[cfg(debug_assertions)]
             let window_url = WebviewUrl::App(Default::default());