Replace counter-arguments with possible answers and unify search inputs.

Models, AI assistant, and UI now show diskussionsfertige Antworten without titles; shared search partial fixes aria-label rendering.

Co-authored-by: Cursor <cursoragent@cursor.com>

templates/claims/home.html

@@ -6,10 +6,7 @@
 <header class="mb-4">
     <h1 class="fk-page-title">Themen</h1>
     <form method="get" action="{% url 'claims:home' %}" class="mb-2" data-live-search data-live-target="#home-results">
-        <div class="input-group">
-            <span class="input-group-text border-end-0"><i class="bi bi-search"></i></span>
-            <input type="search" name="q" class="form-control border-start-0 ps-0" placeholder="Suchen…" value="{{ query }}" aria-label="Kategorien durchsuchen" autocomplete="off">
-        </div>
+        {% include "claims/partials/search_input.html" with value=query aria_label="Kategorien durchsuchen" %}
     </form>
     <div class="d-flex justify-content-between align-items-center">
         <a href="{% url 'claims:search' %}" class="small text-muted text-decoration-none">Alle Behauptungen</a>