Fix ScheduleManager start() self-deadlock on cached schedule

start() held mutex_ and then called loadCache(), which re-locks the same
non-recursive mutex. When a schedule cache file exists and parses (the
normal case for a provisioned kiosk), this self-deadlocks and blocks
SDL_AppInit before the first frame, leaving only a black screen and the
compositor cursor.

Narrow the lock to the member setup so loadCache() can take the lock
itself. Add a regression test that starts with a cached payload present.

src/schedule/schedule_manager.cpp

@@ -87,16 +87,20 @@ void ScheduleManager::refreshOnce() {
 
 void ScheduleManager::start(db::DatabaseManager& db, const std::string& timezone,
                             std::function<void()> onChanged) {
-    std::lock_guard<std::mutex> lock(mutex_);
-    if (started_) return;
-    started_ = true;
-    db_ = &db;
-    timezone_ = timezone;
-    onChanged_ = std::move(onChanged);
-    licenseKey_ = db.getKV(db::KV_LICENSE_KEY);
-    enabled_ = true; // config supplies the toggle via setEnabled()
+    {
+        std::lock_guard<std::mutex> lock(mutex_);
+        if (started_) return;
+        started_ = true;
+        db_ = &db;
+        timezone_ = timezone;
+        onChanged_ = std::move(onChanged);
+        licenseKey_ = db.getKV(db::KV_LICENSE_KEY);
+        enabled_ = true; // config supplies the toggle via setEnabled()
+    }
 
-    // Offline first: load any cached payload immediately.
+    // Offline first: load any cached payload immediately. Called outside the
+    // lock because loadCache() acquires mutex_ itself; holding it here would
+    // self-deadlock on the non-recursive mutex when a cache file exists.
     loadCache();
 
     stop_.store(false);