feat(api): google tasks oauth, sync engine, and background worker

- ApiClient with manual OAuth2 Device Flow (no yup-oauth2 dependency)
- Devide auth: POST device/code -> show URL+code -> poll token endpoint
- Token persistence in ~/.config/task_app/token.json
- CRUD: create_task, update_task, delete_task, move_task via Google Tasks API
- fetch_lists and fetch_tasks for initial sync import
- Db wraps Connection in std::sync::Mutex for thread-safe sharing via Arc
- Sync engine: background thread with tokio runtime, processes queue every 30s
- process_sync_queue drains sync_queue and calls API methods
- trigger_sync() called after every local mutation (create/update/delete/reorder)
- Network status propagated to UI (Online/Offline/Syncing)
- Initial sync skeleton ready for full import flow

src/app.rs

@@ -1,7 +1,11 @@
-use crossterm::event::{KeyCode, KeyEvent, KeyModifiers};
+use std::sync::Arc;
+
 use chrono::NaiveDateTime;
+use crossterm::event::{KeyCode, KeyEvent, KeyModifiers};
+use tokio::sync::mpsc;
 
 use crate::domain::models::*;
+use crate::infrastructure::api::ApiClient;
 use crate::infrastructure::db::Db;
 use crate::ui::{Focus, NetworkStatus, Popup};
 
@@ -19,11 +23,18 @@ pub struct App {
     pub should_quit: bool,
     pub task_list_scroll: u16,
     pub detail_scroll: u16,
-    pub db: Db,
+    pub db: Arc<Db>,
+    pub api_client: Arc<ApiClient>,
+    sync_tx: mpsc::Sender<SyncCommand>,
+}
+
+pub enum SyncCommand {
+    TriggerSync,
+    Shutdown,
 }
 
 impl App {
-    pub fn new(db: Db) -> Self {
+    pub fn new(db: Arc<Db>, api_client: Arc<ApiClient>, sync_tx: mpsc::Sender<SyncCommand>) -> Self {
         let lists = db.get_lists();
         let tasks = if !lists.is_empty() {
             let list_id = &lists[0].id;
@@ -47,9 +58,15 @@ impl App {
             task_list_scroll: 0,
             detail_scroll: 0,
             db,
+            api_client,
+            sync_tx,
         }
     }
 
+    fn trigger_sync(&self) {
+        let _ = self.sync_tx.try_send(SyncCommand::TriggerSync);
+    }
+
     pub fn handle_key(&mut self, key: KeyEvent) {
         if let Some(ref popup) = self.show_popup.clone() {
             self.handle_popup_key(key, popup);
@@ -167,6 +184,7 @@ impl App {
                                     &list.id,
                                     &serde_json::to_string(&list).unwrap_or_default(),
                                 ).ok();
+                                self.trigger_sync();
                                 self.load_lists();
                             }
                             Focus::TaskList => {
@@ -188,13 +206,14 @@ impl App {
                                         list_id,
                                         &serde_json::to_string(&task).unwrap_or_default(),
                                     ).ok();
+                                    self.trigger_sync();
                                     self.load_tasks();
                                 }
                             }
                             Focus::Detail => {
                                 if !self.tasks.is_empty() {
                                     let task = &mut self.tasks[self.selected_task];
-                            task.title = input;
+                                    task.title = input;
                                     self.db.update_task(task).ok();
                                     self.db.push_sync(
                                         SyncAction::Update,
@@ -202,9 +221,8 @@ impl App {
                                         &task.list_id,
                                         &serde_json::to_string(task).unwrap_or_default(),
                                     ).ok();
+                                    self.trigger_sync();
                                     self.load_tasks();
-                                    if !self.tasks.is_empty() && self.selected_task < self.tasks.len() {
-                                    }
                                 }
                             }
                         }
@@ -257,6 +275,7 @@ impl App {
                             &task.list_id,
                             &serde_json::to_string(task).unwrap_or_default(),
                         ).ok();
+                        self.trigger_sync();
                         self.load_tasks();
                     }
                     self.show_popup = None;
@@ -285,6 +304,7 @@ impl App {
                                     &list_id,
                                     "",
                                 ).ok();
+                                self.trigger_sync();
                                 self.load_lists();
                                 if self.selected_list >= self.lists.len() {
                                     self.selected_list = self.lists.len().saturating_sub(1);
@@ -304,6 +324,7 @@ impl App {
                                     &list_id,
                                     "",
                                 ).ok();
+                                self.trigger_sync();
                                 self.load_tasks();
                                 if self.selected_task >= self.tasks.len() {
                                     self.selected_task = self.tasks.len().saturating_sub(1);
@@ -354,6 +375,7 @@ impl App {
                 &list_id,
                 &payload.to_string(),
             ).ok();
+            self.trigger_sync();
             self.selected_task = new_index as usize;
             self.load_tasks();
         }