Add YouTrack pull/push sync with project settings and time tracking.

Wire manual Y menu and CLI sync for issues and work items, persist
per-project credentials, and keep local edits until an explicit push.

Co-authored-by: Cursor <cursoragent@cursor.com>

internal/ticket/jsonstore_test.go

@@ -4,6 +4,7 @@ import (
 	"os"
 	"path/filepath"
 	"testing"
+	"time"
 
 	"task/internal/ticket"
 )
@@ -65,6 +66,43 @@ func TestJSONStoreCreateListUpdate(t *testing.T) {
 	}
 }
 
+func TestUpdateAfterMarkSyncedIsDirty(t *testing.T) {
+	store := ticket.NewJSONStore(t.TempDir())
+	created, err := store.Create(ticket.Ticket{
+		Title: "Synced", ProjectID: "inbox", Status: ticket.StatusTodo,
+		Source: ticket.SourceYouTrack, ExternalID: "TAS-1",
+	})
+	if err != nil {
+		t.Fatal(err)
+	}
+	if err := store.MarkSynced(created.ID); err != nil {
+		t.Fatalf("MarkSynced: %v", err)
+	}
+	synced, err := store.Get(created.ID)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if synced.UpdatedAt.After(synced.SyncedAt) {
+		t.Fatalf("freshly marked synced should not be dirty: updated=%v syncedAt=%v",
+			synced.UpdatedAt, synced.SyncedAt)
+	}
+
+	// Simulate UI edit: copy ticket (SyncedAt == UpdatedAt) and change title.
+	edited := synced
+	edited.Title = "Edited locally"
+	time.Sleep(time.Millisecond) // ensure clock can move
+	if err := store.Update(edited); err != nil {
+		t.Fatal(err)
+	}
+	got, err := store.Get(created.ID)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !got.UpdatedAt.After(got.SyncedAt) {
+		t.Fatalf("edit must bump UpdatedAt past SyncedAt: %v vs %v", got.UpdatedAt, got.SyncedAt)
+	}
+}
+
 func TestJSONStoreMigratesLegacyTasksJSON(t *testing.T) {
 	dir := t.TempDir()
 	projectDir := filepath.Join(dir, "projects", "inbox")