auth: two-step sign-in (TOTP) for admins, with recovery codes

auth/totp.ts per 08 §2.4: RFC 6238 (HMAC-SHA1, 30 s, 6 digits, ±1
step) with node:crypto only, checked against the RFC's test vectors.
Migration 0003: users.totp_recovery_hashes and totp_last_step.

Admins turn it on from My account (the header's "Account"): scan the
QR or type the key, confirm a code, get 10 recovery codes once. Login
asks for the code only after the password is right (401 totp_required,
no session); a wrong code is a failed login (rate limit, audit). A
step signs in once (totp_last_step updated atomically) and a recovery
code once (array_remove guarded by any()). Off and new codes need the
password; another admin can turn it off for a lost phone, which signs
that user out. Users list shows it (twoStep).

Also, found by the full e2e chain on one shared database:
- Linphone tokens: only the exact token issued is accepted. The last
  base64 character can carry ignored bits, so another spelling decoded
  to the same signed token.
- Test scripts no longer assume a fresh system: m3-t3 picks Dan in the
  test box, m8-check dials whatever slot the park took (findslot =
  next), m10-t4 uses the admin's existing extension, m11-t1 clears the
  public IP on its own first (local nets are in the transports while
  one is set, and transports change only on a restart).

e2e m11-t1-totp; the full chain M1-M11 (33 scripts) passes.

Task: M11-T1

packages/shared/src/auth.ts

@@ -6,10 +6,8 @@ export const PASSWORD_MIN = 10;
 export const LoginSchema = z.object({
   email: z.string().trim().min(3, 'Enter your email').max(254),
   password: z.string().min(1, 'Enter your password').max(200),
-  totp: z
-    .string()
-    .regex(/^\d{6}$/)
-    .optional(), // M11
+  /** The authenticator code, or a recovery code ("k7m3q-x9tpw"), when two-step sign-in is on. */
+  totp: z.string().trim().max(20).optional(),
 });
 
 export const ChangePasswordSchema = z.object({
@@ -31,3 +29,16 @@ export type AuthUser = {
   mustChangePassword: boolean;
   extension: { id: string; number: string; name: string } | null;
 };
+
+/** Two-step sign-in (TOTP, 08 §2.4) for the signed-in user. */
+export type TotpStatus = { enabled: boolean; recoveryCodesLeft: number };
+/** Start: the secret to scan (not stored until a code confirms it). */
+export type TotpSetup = { secret: string; otpauthUrl: string; qr: string };
+export const TotpEnableSchema = z.object({
+  secret: z.string().regex(/^[A-Z2-7]{32}$/),
+  code: z
+    .string()
+    .trim()
+    .regex(/^\d{6}$/, 'The 6-digit code from the app'),
+});
+export const PasswordConfirmSchema = z.object({ password: z.string().min(1).max(200) });

packages/shared/src/users.ts

@@ -29,6 +29,8 @@ export type UserDto = {
   role: 'admin' | 'user';
   isActive: boolean;
   mustChangePassword: boolean;
+  /** Two-step sign-in (TOTP) is on. */
+  twoStep: boolean;
   lastLoginAt: string | null;
   createdAt: string;
   extension: { id: string; number: string } | null;