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.

tests/test_schedule_engine.cpp

@@ -297,6 +297,34 @@ TEST(ScheduleManagerTest, OfflineFallsBackToCache) {
     radiantwave::sync::schedule_cache::clear();
 }
 
+// Regression: start() must not deadlock when a cache file is present. It used
+// to hold mutex_ and then call loadCache(), which re-locked the same
+// non-recursive mutex (self-deadlock), blocking SDL_AppInit before the first
+// frame was ever presented — the kiosk sat on a black screen.
+TEST(ScheduleManagerTest, StartWithCachedPayloadDoesNotDeadlock) {
+    const std::string dir = tempCacheDir();
+    setenv("HOME", dir.c_str(), 1);
+
+    SchedulePayload p = dailyPayload();
+    ASSERT_TRUE(radiantwave::sync::schedule_cache::write(p, "\"cached\""));
+
+    const std::string dbPath =
+        (std::filesystem::temp_directory_path() / "rw_schedule_start_test.db")
+            .string();
+    std::filesystem::remove(dbPath);
+    radiantwave::db::DatabaseManager db;
+    ASSERT_TRUE(db.initialize(dbPath));
+
+    radiantwave::schedule::ScheduleManager manager;
+    manager.start(db, "UTC");
+    EXPECT_TRUE(manager.hasSchedule());
+    manager.shutdown();
+
+    db.close();
+    std::filesystem::remove(dbPath);
+    radiantwave::sync::schedule_cache::clear();
+}
+
 // ─── Phase 5: consume real Portal-generated payloads ───────────────────
 //
 // These fixtures were captured from a running Portal (GET