Track preschool planning days, partner invites and real vacation forfeiture

Three strands of work that grew together across the same settings screen and
API client, so they land as one change.

Per-year preschool planning days ("studiedagar"): new table, repository
(SQLite + Postgres), service, router and migration 007, plus the hooks and
Settings UI to plan and record them per child and year. Allocation now
reserves the recorded figure for a year where one exists and only falls back
to the child-level estimate otherwise, marking that fallback as assumed.

Partner invitations: workspaces issue and list invitations, registration
accepts an invite token to join the inviter's workspace instead of creating a
personal one, and a /join/:token page plus the settings invite panel drive it.

Vacation forfeiture: tips and the dashboard now distinguish days a parent
genuinely loses from days that merely age, so the warning stops firing on
balances that were never at risk.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

backend/app/routers/auth.py

@@ -13,7 +13,7 @@ from app.dependencies import (
 )
 from app.rate_limit import limiter
 from app.models.auth import LoginRequest, RegisterRequest, TokenResponse, UserMeResponse
-from app.utils.errors import AuthError, ConflictError, UnauthorizedError
+from app.utils.errors import AuthError, ConflictError, InvitationError, UnauthorizedError
 
 router = APIRouter(prefix="/api/auth", tags=["auth"])
 
@@ -31,9 +31,12 @@ async def register(
             email=str(payload.email),
             password=payload.password,
             display_name=payload.display_name,
+            invite_token=payload.invite_token,
         )
     except ConflictError as exc:
         raise HTTPException(status.HTTP_409_CONFLICT, str(exc)) from exc
+    except InvitationError as exc:
+        raise HTTPException(status.HTTP_400_BAD_REQUEST, str(exc)) from exc
 
     access = service.create_access_token(user.id)
     refresh = service.create_refresh_token(user.id)