feat(billing): add percentage discount coupons

Admins can create coupon codes that discount specific services (app
runtimes, optional services, managed products, custom-domain addon, or
all) and restrict them to specific users or make them public, with total
and per-user usage caps and an active date window.

Coupons apply in deploy, renewal, and upgrade flows: cost-breakdown lines
are tagged with a service key, the eligible portion is discounted and
capped to the payable amount, the invoice records discountAmount/
discountCode, and the redemption is recorded once when the invoice is
fully paid (covering wallet, gateway, and mixed payments).

- Discount + DiscountRedemption entities; invoice discount columns
- DiscountService (CRUD, validation, redemption) + admin/validate API
- Idempotent schema bootstrap on init so production (synchronize off)
  provisions the tables/columns without a migration runner
- Admin discounts UI, coupon entry in deploy/renewal, invoice discount line
- fa/en strings; discount.service unit spec

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

frontend/src/types/index.ts

@@ -704,12 +704,49 @@ export interface CatalogOptionalServiceOption {
   label: string;
 }
 
+export interface DiscountServiceOption {
+  value: string;
+  label: string;
+  group: string;
+}
+
 export interface PricingCatalog {
   runtimes: Record<string, PricingRateRow[]>;
   optionalServices: Record<string, OptionalServiceCatalogEntry>;
   customDomain: CustomDomainCatalogRow;
   runtimeOptions: CatalogRuntimeOption[];
   optionalServiceOptions: CatalogOptionalServiceOption[];
+  discountServiceOptions: DiscountServiceOption[];
+}
+
+export interface Discount {
+  id: string;
+  code: string;
+  name: string;
+  description?: string;
+  percentOff: number;
+  services: string[];
+  isPublic: boolean;
+  allowedUserIds: string[];
+  maxUses: number | null;
+  maxUsesPerUser: number | null;
+  usedCount: number;
+  startsAt: string | null;
+  endsAt: string | null;
+  isActive: boolean;
+  createdAt: string;
+  updatedAt: string;
+}
+
+/** Result of POST /billing/discounts/validate */
+export interface DiscountValidation {
+  valid: boolean;
+  reason?: string;
+  code?: string;
+  name?: string;
+  percentOff?: number;
+  eligibleAmount?: number;
+  discountAmount?: number;
 }
 
 export interface WalletBalance {
@@ -753,6 +790,8 @@ export interface Invoice {
   status: InvoiceStatus;
   paymentMethod?: PaymentMethod;
   subtotal: number;
+  discountAmount?: number;
+  discountCode?: string;
   total: number;
   paidAmount: number;
   dueAmount: number;
@@ -794,6 +833,15 @@ export interface DeployExtraChargeLine {
   fullPeriodAmount?: number;
 }
 
+export interface CouponDiscountPreview {
+  valid: boolean;
+  reason?: string;
+  code?: string;
+  name?: string;
+  percentOff?: number;
+  discountAmount?: number;
+}
+
 export interface DeployCostPreview extends CostBreakdown {
   cycle: BillingCycle;
   fullAmount: number;
@@ -805,6 +853,8 @@ export interface DeployCostPreview extends CostBreakdown {
   prepaidCreditUsed: boolean;
   prorateRemainingDays?: number;
   proratePeriodDays?: number;
+  couponDiscount?: CouponDiscountPreview | null;
+  amountDueAfterDiscount?: number;
 }
 
 // ─── Snapshot / Rollback types ──────────────────────