desktop: reminders reach you when the window isn't in front

A Rust worker reads due reminders from the local store every 15 s and
announces each occurrence once: always to the main window as a toast, and
as a system notification (tauri-plugin-notification) when that window
isn't focused. The page no longer polls on the desktop; its Notification
went nowhere in WebKitGTK and its timer stopped with the window. The
Reminders page says what each surface actually does.

Core gains store::due_reminders, compared by instant, not by string.

Refs #5171

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

frontend/src/desktop/bridge.ts

@@ -295,3 +295,27 @@ export async function onCaptured(handler: () => void): Promise<() => void> {
   if (!events) return () => {};
   return events.listen(CAPTURED_EVENT, () => handler());
 }
+
+/** A reminder the desktop's reminder worker found due (desktop/src-tauri/src/reminders.rs). */
+export interface DueReminder {
+  id: string;
+  title: string;
+  remind_at: string;
+  due_ms: number;
+}
+
+/** Fired at the main window for each reminder occurrence, once. */
+const REMINDER_DUE_EVENT = "inkwell://reminder-due";
+
+/**
+ * Run `handler` for each reminder the desktop announces. On the desktop the Rust
+ * worker decides what is due, and raises the system notification itself when the
+ * window isn't in front; the page only shows its toast.
+ *
+ * Returns an unlisten function, or a no-op where there is no event API.
+ */
+export async function onReminderDue(handler: (reminder: DueReminder) => void): Promise<() => void> {
+  const events = window.__TAURI__?.event;
+  if (!events) return () => {};
+  return events.listen<DueReminder>(REMINDER_DUE_EVENT, (e) => handler(e.payload));
+}