Add adaptive FPS and honest device reachability during streaming

DDP uses fire-and-forget UDP, so when a WiFi device becomes overwhelmed
by sustained traffic, sends appear successful while the device is
actually unreachable. This adds:

- HTTP liveness probe (GET /json/info, 2s timeout) every 10s during
  streaming, exposed as device_streaming_reachable in target state
- Adaptive FPS (opt-in): exponential backoff when device is unreachable,
  gradual recovery when it stabilizes — finds sustainable send rate
- Honest health checks: removed the lie that forced device_online=true
  during streaming; now runs actual health checks regardless
- Target editor toggle, FPS display shows effective rate when throttled,
  health dot reflects streaming reachability, red highlight when
  unreachable
- Auto-backup scheduling support in settings modal

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

server/src/wled_controller/main.py

@@ -29,6 +29,8 @@ import wled_controller.core.audio  # noqa: F401 — trigger engine auto-registra
 from wled_controller.storage.value_source_store import ValueSourceStore
 from wled_controller.storage.profile_store import ProfileStore
 from wled_controller.core.profiles.profile_engine import ProfileEngine
+from wled_controller.core.backup.auto_backup import AutoBackupEngine
+from wled_controller.api.routes.system import STORE_MAP
 from wled_controller.utils import setup_logging, get_logger
 
 # Initialize logging
@@ -101,6 +103,14 @@ async def lifespan(app: FastAPI):
     # Create profile engine (needs processor_manager)
     profile_engine = ProfileEngine(profile_store, processor_manager)
 
+    # Create auto-backup engine
+    auto_backup_engine = AutoBackupEngine(
+        settings_path=Path("data/auto_backup_settings.json"),
+        backup_dir=Path("data/backups"),
+        store_map=STORE_MAP,
+        storage_config=config.storage,
+    )
+
     # Initialize API dependencies
     init_dependencies(
         device_store, template_store, processor_manager,
@@ -114,6 +124,7 @@ async def lifespan(app: FastAPI):
         value_source_store=value_source_store,
         profile_store=profile_store,
         profile_engine=profile_engine,
+        auto_backup_engine=auto_backup_engine,
     )
 
     # Register devices in processor manager for health monitoring
@@ -154,6 +165,9 @@ async def lifespan(app: FastAPI):
     # Start profile engine (evaluates conditions and auto-starts/stops targets)
     await profile_engine.start()
 
+    # Start auto-backup engine (periodic configuration backups)
+    await auto_backup_engine.start()
+
     # Auto-start targets with auto_start=True
     auto_started = 0
     for target in targets:
@@ -172,6 +186,12 @@ async def lifespan(app: FastAPI):
     # Shutdown
     logger.info("Shutting down LED Grab")
 
+    # Stop auto-backup engine
+    try:
+        await auto_backup_engine.stop()
+    except Exception as e:
+        logger.error(f"Error stopping auto-backup engine: {e}")
+
     # Stop profile engine first (deactivates profile-managed targets)
     try:
         await profile_engine.stop()