fix(filters): improve base model filtering UX

templates/components/header.html

@@ -145,9 +145,22 @@
 
   <div class="filter-section">
     <h4>{{ t('header.filter.baseModel') }}</h4>
+    <input
+      type="text"
+      id="baseModelSearchInput"
+      class="filter-search-input"
+      placeholder="{{ t('header.filter.baseModelSearchPlaceholder') }}"
+      autocomplete="off"
+      autocorrect="off"
+      autocapitalize="none"
+      spellcheck="false"
+    >
     <div class="filter-tags" id="baseModelTags">
       <!-- Tags will be dynamically inserted here -->
     </div>
+    <div id="baseModelEmptyState" class="filter-empty-state" hidden>
+      {{ t('header.filter.noBaseModelMatches') }}
+    </div>
   </div>
   <div class="filter-section">
     <div class="filter-section-header">
@@ -188,4 +201,4 @@
       {{ t('header.filter.clearAll') }}
     </button>
   </div>
-</div>
+</div>