The integration no longer owns a database

The HA integration is now purely a client of the NestQuest API service
(Feature 18): the API owns the SQLite file, the migrations, and every
business rule, so keeping a second copy of that ownership inside the
integration meant two sources of truth for household state, dead
wiring (the startup backfill, the day-rollover materialization and
sweep listeners, the corrupt-DB handling, the admin-allowlist seeding)
and settings keys nothing consumes any more.

Removed the integration's re-export/DB shim modules (db, store,
migrations, schema, the five DAOs, completion, children,
quest_definitions, admin_allowlist, presence, presence_management,
materialize, recurrence, events, sweep); the bundled domain package at
custom_components/nestquest/core/ is untouched and remains the single
home of those engines.  Setup now builds only the API client, the
snapshot coordinator, and the SSE subscription, registers the one
complete_quest proxy, and forwards the platforms.  The options flow
keeps only the keys the client itself consumes (API base URL + panel
token, update interval, staleness, panel idle timeout); the horizon,
rollover, notification and admin-allowlist settings moved out with the
database (the API's settings store owns horizon/rollover, and the
automations take their behaviour from blueprint inputs).  The
integration-plane tests now script the panel route's payloads and SSE
frames instead of seeding a local database; the core-plane tests keep
their coverage with imports pointed at core directly.

tests/test_children_registry.py

@@ -8,16 +8,16 @@ from unittest.mock import AsyncMock, MagicMock
 
 import pytest
 
-from custom_components.nestquest.children import (
+from custom_components.nestquest.core.children import (
     create_child,
     edit_child,
     list_children,
     reorder_children,
     set_child_active,
 )
-from custom_components.nestquest.dao_children import ChildRecord, ChildrenDao
-from custom_components.nestquest.db import NestQuestDatabase
-from custom_components.nestquest.migrations import apply_migrations
+from custom_components.nestquest.core.dao_children import ChildRecord, ChildrenDao
+from custom_components.nestquest.core.db import NestQuestDatabase
+from custom_components.nestquest.core.migrations import apply_migrations
 
 
 def _run(coro):
@@ -739,12 +739,12 @@ def test_deactivating_child_preserves_definitions_instances_events(
     async def _body(database):
         from datetime import date, timedelta
 
-        from custom_components.nestquest.dao_children import ChildrenDao
-        from custom_components.nestquest.dao_instances import (
+        from custom_components.nestquest.core.dao_children import ChildrenDao
+        from custom_components.nestquest.core.dao_instances import (
             CompletionEventsDao,
             QuestInstancesDao,
         )
-        from custom_components.nestquest.dao_rules import (
+        from custom_components.nestquest.core.dao_rules import (
             QuestDefinitionsDao,
             ScheduleRulesDao,
         )
@@ -831,7 +831,7 @@ def test_no_code_path_deletes_a_child_row() -> None:
 
     import inspect
 
-    from custom_components.nestquest.dao_children import ChildrenDao
+    from custom_components.nestquest.core.dao_children import ChildrenDao
 
     methods = {
         name