Add a plan sync endpoint that recomputes, persists and reports the delta

The calendar is becoming the plan: a user edits a period and the schedule
updates immediately, with no separate propose and apply steps. POST
/api/plan/sync does both and returns a per-date diff against a snapshot taken
before any write, so the interface can say what actually moved rather than
guessing from coarse counters.

Pinned days now mean something. A day the user hand-edited keeps its type and
its parent: the loader hides unpinned wish-attributed rows from the allocator
so a re-plan is free to move them, while pinned rows stay visible and the
existing occupancy check refuses to touch them. Their cost is debited off the
pool before any window is funded, following the precedent already set for
preschool planning days.

Propose and apply are untouched. The allocator stays pure.

backend/tests/conftest.py

@@ -32,6 +32,7 @@ from app.repositories_impl.sqlite.workspace_repository import (
     SQLiteWorkspaceInvitationRepository,
     SQLiteWorkspaceRepository,
 )
+from app.services.allocation_service import AllocationInputLoader, PlanningEngineService
 from app.services.analytics_service import AnalyticsService
 from app.services.auth_service import AuthService
 from app.services.child_service import ChildService
@@ -262,10 +263,43 @@ async def analytics_service(
     )
 
 
+@pytest_asyncio.fixture
+async def allocation_input_loader(
+    workspace_repo: SQLiteWorkspaceRepository,
+    child_repo: SQLiteChildRepository,
+    personal_data_repo: SQLitePersonalDataRepository,
+    parental_leave_repo: SQLiteParentalLeaveRepository,
+    vacation_repo: SQLiteVacationDaysRepository,
+    planned_leave_repo: SQLitePlannedLeaveRepository,
+    leave_wish_repo: SQLiteLeaveWishRepository,
+    day_override_repo: SQLiteDayOverrideRepository,
+) -> AllocationInputLoader:
+    return AllocationInputLoader(
+        workspace_repo=workspace_repo,
+        child_repo=child_repo,
+        personal_data_repo=personal_data_repo,
+        parental_leave_repo=parental_leave_repo,
+        vacation_repo=vacation_repo,
+        planned_leave_repo=planned_leave_repo,
+        leave_wish_repo=leave_wish_repo,
+        day_override_repo=day_override_repo,
+    )
+
+
+@pytest_asyncio.fixture
+async def planning_engine_service(
+    allocation_input_loader: AllocationInputLoader,
+) -> PlanningEngineService:
+    return PlanningEngineService(allocation_input_loader)
+
+
 @pytest_asyncio.fixture
 async def planning_service(
     planned_leave_repo: SQLitePlannedLeaveRepository,
     analytics_service: AnalyticsService,
     parental_leave_repo: SQLiteParentalLeaveRepository,
+    planning_engine_service: PlanningEngineService,
 ) -> PlanningService:
-    return PlanningService(planned_leave_repo, analytics_service, parental_leave_repo)
+    return PlanningService(
+        planned_leave_repo, analytics_service, parental_leave_repo, planning_engine_service
+    )