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.

Replit-Task-Id: 475a7439-b357-400d-805f-5f2fda20ed24

lib/api-spec/openapi.yaml

@@ -245,6 +245,31 @@ paths:
               schema:
                 $ref: "#/components/schemas/AuthUser"
 
+  /auth/me/clock-style:
+    patch:
+      operationId: updateClockStyle
+      tags: [auth]
+      summary: Update preferred home-screen clock style
+      requestBody:
+        required: true
+        content:
+          application/json:
+            schema:
+              $ref: "#/components/schemas/UpdateClockStyleBody"
+      responses:
+        "200":
+          description: Updated
+          content:
+            application/json:
+              schema:
+                $ref: "#/components/schemas/AuthUser"
+        "400":
+          description: Validation error
+          content:
+            application/json:
+              schema:
+                $ref: "#/components/schemas/ErrorResponse"
+
   # Apps
   /apps:
     get:
@@ -970,6 +995,22 @@ components:
       required:
         - language
 
+    ClockStyle:
+      type: string
+      enum: [full, digital, digital-no-seconds, analog, minimal]
+      description: Per-user home-screen clock style preference
+
+    UpdateClockStyleBody:
+      type: object
+      properties:
+        clockStyle:
+          oneOf:
+            - $ref: "#/components/schemas/ClockStyle"
+            - type: "null"
+          description: Clock style; pass null to clear and use the default
+      required:
+        - clockStyle
+
     AuthUser:
       type: object
       properties:
@@ -985,6 +1026,10 @@ components:
           type: ["string", "null"]
         preferredLanguage:
           type: string
+        clockStyle:
+          oneOf:
+            - $ref: "#/components/schemas/ClockStyle"
+            - type: "null"
         avatarUrl:
           type: ["string", "null"]
         isActive:
@@ -1020,6 +1065,10 @@ components:
           type: ["string", "null"]
         preferredLanguage:
           type: string
+        clockStyle:
+          oneOf:
+            - $ref: "#/components/schemas/ClockStyle"
+            - type: "null"
         avatarUrl:
           type: ["string", "null"]
         isActive: