fix(settings): the offline language mirror does not outlive the account (#2146)

The mirror of the account language stayed in localStorage past logout, so the next account on the device booted in the previous user's language forever. It is cleared on logout and rewritten on login, and the rate-limit message follows the same order the boot language does.

client/tests/unit/stores/authStore.test.ts

@@ -759,4 +759,20 @@ describe('authStore', () => {
       expect(syncTriggers.registerSyncTriggers).toHaveBeenCalled();
     });
   });
+
+  // The mirror of the account's server-side language is a per-device copy like the
+  // appearance snapshot and the startup destination, and gets dropped with them.
+  // 'app_language' is not a mirror but this device's own choice, so it stays.
+  describe('FE-STORE-AUTH-034: logout drops the language mirror', () => {
+    it('clears the account language but keeps an explicit in-app choice', async () => {
+      localStorage.setItem('app_language_server', 'ja');
+      localStorage.setItem('app_language', 'de');
+      useAuthStore.setState({ user: buildUser(), isAuthenticated: true });
+
+      await useAuthStore.getState().logout();
+
+      expect(localStorage.getItem('app_language_server')).toBeNull();
+      expect(localStorage.getItem('app_language')).toBe('de');
+    });
+  });
 });