feat(api): add PATCH endpoint and fix preferences API paths

- Add PATCH method to PreferencesController for partial updates
- Fix profile page API path: /users/me/preferences → /api/users/me/preferences
- Fix appearance page API path: same prefix correction
- Add controller and service spec files

Closes SS-API-002

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

apps/web/src/app/(authenticated)/profile/page.tsx

@@ -103,7 +103,7 @@ export default function ProfilePage(): ReactElement {
     setPrefsError(null);
 
     try {
-      const data = await apiGet<UserPreferences>("/users/me/preferences");
+      const data = await apiGet<UserPreferences>("/api/users/me/preferences");
       setPreferences(data);
     } catch (err: unknown) {
       const message = err instanceof Error ? err.message : "Could not load preferences";

apps/web/src/app/(authenticated)/settings/appearance/page.tsx

@@ -240,7 +240,7 @@ export default function AppearanceSettingsPage(): ReactElement {
       setLocalTheme(themeId);
       setSaving(true);
       try {
-        await apiPatch("/users/me/preferences", { theme: themeId });
+        await apiPatch("/api/users/me/preferences", { theme: themeId });
       } catch {
         // Theme is still applied locally even if API save fails
       } finally {