Add OpenAPI docs, frontend, migrations, and API updates

- OpenAPI: add missing endpoints (add-from-url, subscriptions, public availability)
- OpenAPI: CalendarSubscription schema, Subscriptions tag
- Frontend app
- Migrations: count_for_availability, subscriptions_sync, user_preferences, calendar_settings
- Config, rate limit, auth, calendar, booking, ICS, availability, user service updates

Made-with: Cursor

internal/scheduler/worker.go

@@ -11,6 +11,11 @@ import (
 	"github.com/hibiken/asynq"
 )
 
+// SubscriptionSyncer performs a subscription sync (used by background worker).
+type SubscriptionSyncer interface {
+	SyncSubscriptionBackground(ctx context.Context, subscriptionID string) error
+}
+
 type ReminderWorker struct {
 	queries *repository.Queries
 }
@@ -41,14 +46,35 @@ func (w *ReminderWorker) HandleReminderTask(ctx context.Context, t *asynq.Task)
 	return nil
 }
 
-func StartWorker(redisAddr string, worker *ReminderWorker) *asynq.Server {
+type SubscriptionSyncWorker struct {
+	syncer SubscriptionSyncer
+}
+
+func NewSubscriptionSyncWorker(syncer SubscriptionSyncer) *SubscriptionSyncWorker {
+	return &SubscriptionSyncWorker{syncer: syncer}
+}
+
+func (w *SubscriptionSyncWorker) HandleSubscriptionSync(ctx context.Context, t *asynq.Task) error {
+	var payload SubscriptionSyncPayload
+	if err := json.Unmarshal(t.Payload(), &payload); err != nil {
+		return fmt.Errorf("unmarshal subscription sync payload: %w", err)
+	}
+	if err := w.syncer.SyncSubscriptionBackground(ctx, payload.SubscriptionID); err != nil {
+		return fmt.Errorf("sync subscription %s: %w", payload.SubscriptionID, err)
+	}
+	log.Printf("subscription sync completed: %s", payload.SubscriptionID)
+	return nil
+}
+
+func StartWorker(redisAddr string, worker *ReminderWorker, subSyncWorker *SubscriptionSyncWorker) *asynq.Server {
 	srv := asynq.NewServer(
 		asynq.RedisClientOpt{Addr: redisAddr},
 		asynq.Config{
 			Concurrency: 10,
 			Queues: map[string]int{
-				"reminders": 6,
-				"default":   3,
+				"reminders":     6,
+				"subscriptions": 2,
+				"default":       3,
 			},
 			RetryDelayFunc: asynq.DefaultRetryDelayFunc,
 		},
@@ -56,6 +82,9 @@ func StartWorker(redisAddr string, worker *ReminderWorker) *asynq.Server {
 
 	mux := asynq.NewServeMux()
 	mux.HandleFunc(TypeReminder, worker.HandleReminderTask)
+	if subSyncWorker != nil {
+		mux.HandleFunc(TypeSubscriptionSync, subSyncWorker.HandleSubscriptionSync)
+	}
 
 	go func() {
 		if err := srv.Run(mux); err != nil {