security: MFA backup codes — issue on enable, redeem at login, regenerate on demand (#43)

Adds a one-time-use backup code set so users with a lost authenticator are not
locked out. Codes are Crockford base32 (XXXXX-XXXXX), hashed with argon2id, and
redeemed under a WHERE-guarded delete so a concurrent replay race fails closed.

- New MfaBackupCode model + migration
- Issue 10 codes inside the enable transaction; show plaintext exactly once
- Sign-in page accepts TOTP or backup code, reporting remaining count
- regenerateBackupCodes tRPC mutation wipes + reissues atomically
- Unit coverage for generator, normalizer, verify, redeem, and race path

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

packages/api/src/__tests__/user-router.test.ts

@@ -55,6 +55,12 @@ function createAdminCaller(db: Record<string, unknown>) {
   // Individual tests can override by passing their own `activeSession` key.
   const dbWithDefaults = {
     activeSession: { deleteMany: vi.fn().mockResolvedValue({ count: 0 }) },
+    mfaBackupCode: {
+      deleteMany: vi.fn().mockResolvedValue({ count: 0 }),
+      createMany: vi.fn().mockResolvedValue({ count: 10 }),
+      count: vi.fn().mockResolvedValue(0),
+    },
+    $transaction: vi.fn(async (ops: unknown[]) => ops),
     ...db,
   };
   return createCaller({
@@ -735,7 +741,8 @@ describe("user profile and TOTP self-service", () => {
 
     const result = await caller.verifyAndEnableTotp({ token: "123456" });
 
-    expect(result).toEqual({ enabled: true });
+    expect(result.enabled).toBe(true);
+    expect(result.backupCodes).toHaveLength(10);
     // lastTotpAt is written atomically by updateMany (the replay guard);
     // user.update only toggles the enabled flag after the CAS succeeds.
     expect(updateMany).toHaveBeenCalledWith(
@@ -1035,11 +1042,16 @@ describe("user column preferences and MFA status", () => {
       user: {
         findUnique,
       },
+      mfaBackupCode: {
+        deleteMany: vi.fn(),
+        createMany: vi.fn(),
+        count: vi.fn().mockResolvedValue(4),
+      },
     });
 
     const result = await caller.getMfaStatus();
 
-    expect(result).toEqual({ totpEnabled: true });
+    expect(result).toEqual({ totpEnabled: true, backupCodesRemaining: 4 });
     expect(findUnique).toHaveBeenCalledWith({
       where: { id: "user_admin" },
       select: { totpEnabled: true },