feat(tasks): dual-write tasks to SQLite alongside localStorage; boot-load from SQLite on startup

src/lib/stores/page.svelte.js

@@ -201,6 +201,18 @@ function loadTasks() {
 
 export const tasks = $state(loadTasks());
 
+// On boot in the desktop runtime, load canonical tasks from SQLite.
+// localStorage remains the warm cache and fallback.
+if (typeof window !== "undefined" && hasTauriRuntime()) {
+  invoke("list_tasks_cmd")
+    .then((sqliteTasks) => {
+      tasks.length = 0;
+      tasks.push(...sqliteTasks);
+      saveTasks();
+    })
+    .catch(() => {});
+}
+
 export function saveTasks() {
   try {
     localStorage.setItem(TASKS_KEY, JSON.stringify(tasks));
@@ -208,7 +220,7 @@ export function saveTasks() {
 }
 
 export function addTask(task) {
-  tasks.unshift({
+  const newTask = {
     id: crypto.randomUUID(),
     text: task.text,
     bucket: task.bucket || "inbox",
@@ -220,9 +232,20 @@ export function addTask(task) {
     createdAt: new Date().toISOString(),
     sourceTranscriptId: task.sourceTranscriptId || null,
     notes: "",
-  });
+  };
+  tasks.unshift(newTask);
   saveTasks();
   broadcastTasks();
+  if (hasTauriRuntime()) {
+    invoke("create_task_cmd", {
+      request: {
+        id: newTask.id,
+        text: newTask.text,
+        bucket: newTask.bucket,
+        sourceTranscriptId: newTask.sourceTranscriptId,
+      },
+    }).catch(() => {});
+  }
 }
 
 export function updateTask(id, updates) {
@@ -240,15 +263,24 @@ export function deleteTask(id) {
     tasks.splice(idx, 1);
     saveTasks();
     broadcastTasks();
+    if (hasTauriRuntime()) {
+      invoke("delete_task_cmd", { id }).catch(() => {});
+    }
   }
 }
 
 export function completeTask(id) {
   updateTask(id, { done: true, doneAt: new Date().toISOString() });
+  if (hasTauriRuntime()) {
+    invoke("complete_task_cmd", { id }).catch(() => {});
+  }
 }
 
 export function uncompleteTask(id) {
   updateTask(id, { done: false, doneAt: null });
+  if (hasTauriRuntime()) {
+    invoke("uncomplete_task_cmd", { id }).catch(() => {});
+  }
 }
 
 // ---- BroadcastChannel for multi-window task sync ----