feat: invoices — patient billing with installments + PDF export

Backend (new `invoice` RBAC resource, granted to clinicians + reception):
- invoices table (line items + installments as JSONB), types, zod validation,
  service (CRUD + splitIntoInstallments + auto invoice numbers), org-scoped
  REST routes mounted at /api/invoices, activity logging (migration 0015)

Frontend:
- lib/invoices.ts API client + money/date helpers
- /invoices page: list with KPIs and search, create/edit dialog (searchable
  patient combobox, inline line-item editor, live total), detail sheet to split
  a bill into equal monthly installments, delete, and Download PDF
- dependency-free PDF via a print-styled window (browser "Save as PDF")
- sidebar "Invoices" entry under the Patients group; "Added by AI" badge honored

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

backend/src/types/activity.ts

@@ -6,6 +6,7 @@ export type ActivityEntityType =
   | "note"
   | "appointment"
   | "prescription"
+  | "invoice"
   | "inventory"
   | "task";
 

backend/src/types/invoice.ts

@@ -0,0 +1,36 @@
+// The canonical Invoice shape returned by the API. Mirrors the frontend
+// `lib/invoices.ts` Invoice type. Scoped to the active clinic; patient fields
+// are denormalized for display and `fileNumber` links to a patient record.
+export type InvoiceStatus = "draft" | "sent" | "paid" | "void";
+
+export type InvoiceLineItem = {
+  description: string;
+  quantity: number;
+  unitPrice: number;
+};
+
+// One slice of a split bill. `amount` is the installment total; `dueAt` is an
+// optional ISO date; `paid` tracks settlement.
+export type InvoiceInstallment = {
+  label: string;
+  amount: number;
+  dueAt: string | null;
+  paid: boolean;
+};
+
+export type Invoice = {
+  id: string;
+  fileNumber: string;
+  name: string;
+  initials: string;
+  number: string; // human invoice number, e.g. "INV-1001"
+  issuedAt: string; // YYYY-MM-DD
+  dueAt: string | null; // YYYY-MM-DD
+  status: InvoiceStatus;
+  lineItems: InvoiceLineItem[];
+  installments: InvoiceInstallment[];
+  notes: string | null;
+  source: "manual" | "ai";
+  createdAt: string;
+  updatedAt: string;
+};