refactor: setup sidebar header

src/components/refactored/sidebar/utils/search.ts

@@ -0,0 +1,16 @@
+import type { Project } from '@/types/app';
+
+/**
+ * Filters workspaces/projects by matching the search string against
+ * both `displayName` and `name` (case-insensitive substring match).
+ */
+export const filterWorkspacesByName = (workspaces: Project[], filter: string): Project[] => {
+  const normalized = filter.trim().toLowerCase();
+  if (!normalized) return workspaces;
+
+  return workspaces.filter((project) => {
+    const displayName = (project.displayName || project.name).toLowerCase();
+    const projectName = project.name.toLowerCase();
+    return displayName.includes(normalized) || projectName.includes(normalized);
+  });
+};