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/index.ts

@@ -15,6 +15,7 @@ import { appointmentsRouter } from "./routes/appointments.js";
 import { chatRouter } from "./routes/chat.js";
 import { conversationsRouter } from "./routes/conversations.js";
 import { inventoryRouter } from "./routes/inventory.js";
+import { invoicesRouter } from "./routes/invoices.js";
 import { notesRouter } from "./routes/notes.js";
 import { notificationsRouter } from "./routes/notifications.js";
 import { patientsRouter } from "./routes/patients.js";
@@ -63,6 +64,7 @@ app.use("/api/notes", notesRouter);
 app.use("/api/appointments", appointmentsRouter);
 app.use("/api/prescriptions", prescriptionsRouter);
 app.use("/api/inventory", inventoryRouter);
+app.use("/api/invoices", invoicesRouter);
 app.use("/api/tasks", tasksRouter);
 app.use("/api/staff", staffRouter);
 app.use("/api/activity", activityRouter);