fix(home): keep search visible during provider changes

lib/screens/home_search_logic.dart

@@ -137,6 +137,24 @@ class HomeSearchProviderPolicy {
     return resolveProvider(explicitSearchProvider, extensions) != null;
   }
 
+  /// Keeps the Home search surface stable while extension/provider state is
+  /// being reconciled. A transient missing search capability must not remove
+  /// the field above an already-visible Home feed; changing providers should
+  /// never be required just to make Search reappear.
+  static bool shouldShowSearchBar({
+    required bool hasSearchProvider,
+    required bool isSearchProviderLoading,
+    required bool hasHomeFeedExtension,
+    required bool hasExploreContent,
+    required bool hasSearchInput,
+  }) {
+    return hasSearchProvider ||
+        isSearchProviderLoading ||
+        hasHomeFeedExtension ||
+        hasExploreContent ||
+        hasSearchInput;
+  }
+
   static String? sanitizeFilter(
     String? filter,
     String? currentSearchProvider,

lib/screens/home_tab.dart

@@ -768,7 +768,13 @@ class _HomeTabState extends ConsumerState<HomeTab>
       explicitSearchProvider,
       extensions,
     );
-    final showSearchBar = hasSearchProvider || isSearchProviderLoading;
+    final showSearchBar = HomeSearchProviderPolicy.shouldShowSearchBar(
+      hasSearchProvider: hasSearchProvider,
+      isSearchProviderLoading: isSearchProviderLoading,
+      hasHomeFeedExtension: hasHomeFeedExtension,
+      hasExploreContent: hasExploreContent,
+      hasSearchInput: hasSearchInput,
+    );
     final hasResults =
         hasSearchInput || hasActualResults || isLoading || showRecentAccess;
     final showExplore =