fix(nav): header publish menu + userbox card polish

Unpaint multi-type 发布 wrapper, fix light-menu ink, avatar unread
dot clipping, check-in REST double namespace, and user-card VIP/check-in layout.

header.php

@@ -289,7 +289,7 @@ if (!empty($aksrt_bg_styles)) {
 								<button type="button" class="nav-user__toggle navbar-avatar" id="user-menu-toggle" aria-expanded="false" aria-controls="user-dropdown">
 									<?php echo get_avatar(get_current_user_id(), 36, '', esc_attr($aksrt_current_user->display_name), ['loading' => 'lazy']); // phpcs:ignore WordPress.Security.EscapeOutput.OutputNotEscaped ?>
 									<?php if ($aksrt_unread_count > 0) : ?>
-										<span class="nav-user__dot aksrt-notification-badge" aria-hidden="true"></span>
+										<span class="nav-user__dot" aria-hidden="true"></span>
 									<?php endif; ?>
 								</button>
 								<div class="user-dropdown sub-user-box" id="user-dropdown">