feat: migrate storage from JSON files to SQLite

Replace 22 individual JSON store files with a single SQLite database
(data/ledgrab.db). All entity stores now use BaseSqliteStore backed by
SQLite with WAL mode, write-through caching, and thread-safe access.

- Add Database class with SQLite backup/restore API
- Add BaseSqliteStore as drop-in replacement for BaseJsonStore
- Convert all 16 entity stores to SQLite
- Move global settings (MQTT, external URL, auto-backup) to SQLite
  settings table
- Replace JSON backup/restore with SQLite snapshot backups (.db files)
- Remove partial export/import feature (backend + frontend)
- Update demo seed to write directly to SQLite
- Add "Backup Now" button to settings UI
- Remove StorageConfig file path fields (single database_file remains)

server/src/wled_controller/api/dependencies.py

@@ -7,6 +7,7 @@ All getter function signatures remain unchanged for FastAPI Depends() compatibil
 from typing import Any, Dict, TypeVar
 
 from wled_controller.core.processing.processor_manager import ProcessorManager
+from wled_controller.storage.database import Database
 from wled_controller.storage import DeviceStore
 from wled_controller.storage.template_store import TemplateStore
 from wled_controller.storage.postprocessing_template_store import PostprocessingTemplateStore
@@ -129,6 +130,10 @@ def get_weather_manager() -> WeatherManager:
     return _get("weather_manager", "Weather manager")
 
 
+def get_database() -> Database:
+    return _get("database", "Database")
+
+
 # ── Event helper ────────────────────────────────────────────────────────
 
 
@@ -157,6 +162,7 @@ def init_dependencies(
     device_store: DeviceStore,
     template_store: TemplateStore,
     processor_manager: ProcessorManager,
+    database: Database | None = None,
     pp_template_store: PostprocessingTemplateStore | None = None,
     pattern_template_store: PatternTemplateStore | None = None,
     picture_source_store: PictureSourceStore | None = None,
@@ -178,6 +184,7 @@ def init_dependencies(
 ):
     """Initialize global dependencies."""
     _deps.update({
+        "database": database,
         "device_store": device_store,
         "template_store": template_store,
         "processor_manager": processor_manager,