feat: AI-added records save with placeholders + "Added by AI" provenance

Stop blocking AI imports/proposals on missing non-critical fields. Records
the chat agent drafts now save with safe placeholders, auto-generated file
numbers, and a source="ai" marker that surfaces an "Added by AI" badge so a
clinician can review/edit them later.

Backend:
- add `source` (manual|ai) column to patients/appointments/prescriptions
  (migration 0014) + canonical types, services, validation schemas
- relax patient/appointment validation: empty file number allowed, demographic
  + type/provider/initials fall back to placeholders (initials derived from name)
- patients.generateFileNumber() auto-assigns an MRN when one is missing
- proposeAppointment accepts a name when no file number resolves; AI commits +
  /api/ai/import stamp source="ai"

Frontend:
- `source` on Appointment/Patient/Prescription types; AI commits send source="ai"
- reusable <AiBadge> shown on the Patients table/detail and prescriptions list

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

backend/src/lib/initials.ts

@@ -0,0 +1,10 @@
+// Derive up-to-2-character initials from a patient name, for records (e.g. AI
+// imports) that arrive without them. "Ahmed Ali" -> "AA"; "Ahmed" -> "AH".
+export function initialsFromName(name: string): string {
+  const words = name.trim().split(/\s+/).filter(Boolean);
+  if (words.length === 0) return "?";
+  if (words.length === 1) {
+    return (words[0] as string).slice(0, 2).toUpperCase();
+  }
+  return ((words[0]![0] ?? "") + (words.at(-1)![0] ?? "")).toUpperCase();
+}