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/app/routers/plan.py

@@ -15,6 +15,8 @@ from app.models.plan import (
     PlanApplyResponse,
     PlanProposalResponse,
     PlanProposeRequest,
+    PlanSyncRequest,
+    PlanSyncResponse,
 )
 from app.utils.errors import NotFoundError, ValidationError
 
@@ -55,3 +57,23 @@ async def apply_plan(payload: PlanApplyRequest, service: PlanningServiceDep) ->
     except NotFoundError as exc:
         raise HTTPException(status.HTTP_404_NOT_FOUND, str(exc)) from exc
     return PlanApplyResponse.from_domain(result)
+
+
+@router.post("/sync", response_model=PlanSyncResponse)
+async def sync_plan(payload: PlanSyncRequest, service: PlanningServiceDep) -> PlanSyncResponse:
+    """Recompute and persist a workspace's plan in one step.
+
+    The direct-manipulation calendar UX's one call: no separate preview
+    step. Runs propose then apply internally (see
+    `PlanningService.sync_plan`), never retyping or overwriting a day the
+    user has pinned, and reports exactly what changed (`changes`) so the UI
+    can show e.g. "Sommar 2028 flyttades 2 dagar — Ångra" instead of
+    silently rewriting the calendar.
+    """
+    try:
+        result = await service.sync_plan(payload.workspace_id)
+    except NotFoundError as exc:
+        raise HTTPException(status.HTTP_404_NOT_FOUND, str(exc)) from exc
+    except ValidationError as exc:
+        raise HTTPException(status.HTTP_422_UNPROCESSABLE_ENTITY, str(exc)) from exc
+    return PlanSyncResponse.from_domain(result)