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/storage/gradient_store.py

@@ -1,6 +1,6 @@
 """Gradient storage with built-in seeding.
 
-Provides CRUD for gradient entities.  On first run (empty/missing file),
+Provides CRUD for gradient entities.  On first run (empty/missing data),
 seeds 8 built-in gradients matching the legacy hardcoded palettes.
 Built-in gradients are read-only and cannot be deleted or modified.
 """
@@ -9,7 +9,8 @@ import uuid
 from datetime import datetime, timezone
 from typing import List, Optional
 
-from wled_controller.storage.base_store import BaseJsonStore
+from wled_controller.storage.base_sqlite_store import BaseSqliteStore
+from wled_controller.storage.database import Database
 from wled_controller.storage.gradient import Gradient
 from wled_controller.utils import get_logger
 
@@ -43,12 +44,12 @@ def _tuples_to_stops(tuples: list) -> list:
     return [{"position": t[0], "color": [t[1], t[2], t[3]]} for t in tuples]
 
 
-class GradientStore(BaseJsonStore[Gradient]):
-    _json_key = "gradients"
+class GradientStore(BaseSqliteStore[Gradient]):
+    _table_name = "gradients"
     _entity_name = "Gradient"
 
-    def __init__(self, file_path: str):
-        super().__init__(file_path, Gradient.from_dict)
+    def __init__(self, db: Database):
+        super().__init__(db, Gradient.from_dict)
         if not self._items:
             self._seed_builtins()
 
@@ -70,7 +71,7 @@ class GradientStore(BaseJsonStore[Gradient]):
         logger.info(f"Seeded {len(_BUILTIN_DEFS)} built-in gradients")
 
     # Aliases
-    get_all_gradients = BaseJsonStore.get_all
+    get_all_gradients = BaseSqliteStore.get_all
 
     def get_gradient(self, gradient_id: str) -> Gradient:
         return self.get(gradient_id)
@@ -104,7 +105,7 @@ class GradientStore(BaseJsonStore[Gradient]):
             tags=tags or [],
         )
         self._items[gid] = gradient
-        self._save()
+        self._save_item(gid, gradient)
         logger.info(f"Created gradient: {name} ({gid})")
         return gradient
 
@@ -129,7 +130,7 @@ class GradientStore(BaseJsonStore[Gradient]):
         if tags is not None:
             gradient.tags = tags
         gradient.updated_at = datetime.now(timezone.utc)
-        self._save()
+        self._save_item(gradient_id, gradient)
         logger.info(f"Updated gradient: {gradient_id}")
         return gradient