Add per-user clock style preference for the home status bar.

Original task #20: Let each user pick their own home-screen clock
style (analog/digital/minimal/etc.), persisted on the user record
and restored on login / other devices. Default = "full".

Changes:
- DB: added `clock_style varchar(30)` (nullable) to `users`
  (lib/db/src/schema/users.ts) and applied via direct ALTER TABLE
  (drizzle-kit push had unrelated interactive prompts about
  app_opens / user_sessions which were not safe to answer).
- OpenAPI: added `ClockStyle` enum (full/digital/digital-no-seconds
  /analog/minimal), `UpdateClockStyleBody`, exposed `clockStyle`
  on AuthUser and UserProfile, and added PATCH /auth/me/clock-style.
  Regenerated typed client and zod schemas.
- API: `buildAuthUser` and `buildUserProfile` include `clockStyle`;
  new authenticated endpoint updates the current user's style and
  returns the refreshed AuthUser.
- Frontend: new `Clock` component (artifacts/teaboy-os/src/
  components/clock.tsx) with five variants sharing a single `useNow`
  tick hook, plus an SVG analog clock; honors existing
  Latin-digit/locale formatting helpers. New `ClockStylePicker`
  (popover) shown in the status bar with a live preview for each
  option and optimistic update through the AuthUser query cache.
- home.tsx replaces the hard-coded clock block with `<Clock>` driven
  by `user.clockStyle`; trigger button placed next to the language
  toggle.
- i18n: added `home.clockStyle.label` and per-style option labels
  to en.json and ar.json.

Verified via e2e: register → default "full" rendered → switch to
analog → reload → analog persists → switch to minimal → time-only
renders. RTL layout + Latin digits both correct after language
toggle.

artifacts/api-server/src/routes/auth.ts

@@ -15,6 +15,7 @@ import {
   RegisterBody,
   LoginBody,
   UpdateLanguageBody,
+  UpdateClockStyleBody,
   ForgotPasswordBody,
   ResetPasswordBody,
   VerifyResetTokenBody,
@@ -36,6 +37,7 @@ function buildAuthUser(user: typeof usersTable.$inferSelect, roles: string[]) {
     displayNameAr: user.displayNameAr,
     displayNameEn: user.displayNameEn,
     preferredLanguage: user.preferredLanguage,
+    clockStyle: user.clockStyle,
     avatarUrl: user.avatarUrl,
     isActive: user.isActive,
     roles,
@@ -324,4 +326,26 @@ router.patch("/auth/me/language", requireAuth, async (req, res): Promise<void> =
   res.json(buildAuthUser(user, roles));
 });
 
+router.patch("/auth/me/clock-style", requireAuth, async (req, res): Promise<void> => {
+  const parsed = UpdateClockStyleBody.safeParse(req.body);
+  if (!parsed.success) {
+    res.status(400).json({ error: parsed.error.message });
+    return;
+  }
+
+  const [user] = await db
+    .update(usersTable)
+    .set({ clockStyle: parsed.data.clockStyle ?? null })
+    .where(eq(usersTable.id, req.session.userId!))
+    .returning();
+
+  if (!user) {
+    res.status(401).json({ error: "User not found" });
+    return;
+  }
+
+  const roles = await getUserRoles(user.id);
+  res.json(buildAuthUser(user, roles));
+});
+
 export default router;

artifacts/api-server/src/routes/users.ts

@@ -37,6 +37,7 @@ function buildUserProfile(user: typeof usersTable.$inferSelect, roles: string[])
     displayNameAr: user.displayNameAr,
     displayNameEn: user.displayNameEn,
     preferredLanguage: user.preferredLanguage,
+    clockStyle: user.clockStyle,
     avatarUrl: user.avatarUrl,
     isActive: user.isActive,
     roles,