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/api/dependencies.py

@@ -13,8 +13,10 @@ from wled_controller.storage.audio_template_store import AudioTemplateStore
 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
 
 # Global instances (initialized in main.py)
+_auto_backup_engine: AutoBackupEngine | None = None
 _device_store: DeviceStore | None = None
 _template_store: TemplateStore | None = None
 _pp_template_store: PostprocessingTemplateStore | None = None
@@ -121,6 +123,13 @@ def get_profile_engine() -> ProfileEngine:
     return _profile_engine
 
 
+def get_auto_backup_engine() -> AutoBackupEngine:
+    """Get auto-backup engine dependency."""
+    if _auto_backup_engine is None:
+        raise RuntimeError("Auto-backup engine not initialized")
+    return _auto_backup_engine
+
+
 def init_dependencies(
     device_store: DeviceStore,
     template_store: TemplateStore,
@@ -135,12 +144,13 @@ def init_dependencies(
     value_source_store: ValueSourceStore | None = None,
     profile_store: ProfileStore | None = None,
     profile_engine: ProfileEngine | None = None,
+    auto_backup_engine: AutoBackupEngine | None = None,
 ):
     """Initialize global dependencies."""
     global _device_store, _template_store, _processor_manager
     global _pp_template_store, _pattern_template_store, _picture_source_store, _picture_target_store
     global _color_strip_store, _audio_source_store, _audio_template_store
-    global _value_source_store, _profile_store, _profile_engine
+    global _value_source_store, _profile_store, _profile_engine, _auto_backup_engine
     _device_store = device_store
     _template_store = template_store
     _processor_manager = processor_manager
@@ -154,3 +164,4 @@ def init_dependencies(
     _value_source_store = value_source_store
     _profile_store = profile_store
     _profile_engine = profile_engine
+    _auto_backup_engine = auto_backup_engine