feat(13-03): add icon prop to BackendCard and category/search to BackendSelectionStep

- BackendCard accepts optional icon prop rendered in flex row with name
- BackendSelectionStep groups 18 backends into 3 category sections
- Search bar (type=search/searchbox role) filters across displayName, description, category label, field labels
- Empty categories hidden via conditional rendering
- BACKEND_ICONS wired to BackendCard icon prop
- Changed search input to type=search to preserve getByRole('textbox') selector in existing tests

src/components/ui/BackendCard.tsx

@@ -1,13 +1,14 @@
-import type { ButtonHTMLAttributes } from 'react';
+import type { ButtonHTMLAttributes, ReactNode } from 'react';
 
 interface BackendCardProps extends Omit<ButtonHTMLAttributes<HTMLButtonElement>, 'onClick'> {
   name: string;
   description: string;
   selected?: boolean;
   onClick: () => void;
+  icon?: ReactNode;
 }
 
-export function BackendCard({ name, description, selected = false, onClick, ...rest }: BackendCardProps) {
+export function BackendCard({ name, description, selected = false, onClick, icon, ...rest }: BackendCardProps) {
   return (
     <button
       type="button"
@@ -21,7 +22,14 @@ export function BackendCard({ name, description, selected = false, onClick, ...r
       ].join(' ')}
       {...rest}
     >
+      {icon != null ? (
+        <div className="flex items-center gap-2">
+          <span className="w-6 h-6 shrink-0">{icon}</span>
           <span className="font-semibold text-on-surface">{name}</span>
+        </div>
+      ) : (
+        <span className="font-semibold text-on-surface">{name}</span>
+      )}
       <span className="text-sm text-on-surface-container/70">{description}</span>
     </button>
   );

src/components/wizard/BackendSelectionStep.tsx

@@ -1,14 +1,16 @@
-import { useRef } from 'react';
+import { useRef, useState } from 'react';
 import { useForm } from 'react-hook-form';
 import { zodResolver } from '@hookform/resolvers/zod';
 import { z } from 'zod';
+import React from 'react';
 import { useWizard } from '../../store/context';
-import type { BackendType } from '../../store/types';
+import type { BackendType, BackendCategory } from '../../schemas/registry';
 import { BACKEND_REGISTRY } from '../../schemas/registry';
 import { BackendCard } from '../ui/BackendCard';
 import { MD3_BTN_FILLED } from '../../styles/md3-buttons';
 import { TextFieldMD3 } from '../ui/TextFieldMD3';
 import { RemoteNamePreview } from '../ui/RemoteNamePreview';
+import { BACKEND_ICONS } from '../icons/BackendIcons';
 
 const remoteNameSchema = z.object({
   name: z
@@ -22,10 +24,30 @@ const remoteNameSchema = z.object({
 
 type RemoteNameFormValues = z.infer<typeof remoteNameSchema>;
 
+const CATEGORY_ORDER: BackendCategory[] = ['cloud-object-storage', 'cloud-drives', 'protocol-based'];
+const CATEGORY_LABELS: Record<BackendCategory, string> = {
+  'cloud-object-storage': 'Cloud Object Storage',
+  'cloud-drives': 'Cloud Drives',
+  'protocol-based': 'Protocol-based',
+};
+
+function matchesSearch(
+  entry: { displayName: string; description: string; category: BackendCategory; fields: { label: string }[] },
+  query: string
+): boolean {
+  const q = query.toLowerCase();
+  return (
+    entry.displayName.toLowerCase().includes(q) ||
+    entry.description.toLowerCase().includes(q) ||
+    CATEGORY_LABELS[entry.category].toLowerCase().includes(q) ||
+    entry.fields.some(f => f.label.toLowerCase().includes(q))
+  );
+}
 
 export function BackendSelectionStep() {
   const { state, dispatch } = useWizard();
   const pendingBackend = useRef<BackendType | null>(null);
+  const [searchQuery, setSearchQuery] = useState('');
 
   const {
     register,
@@ -77,17 +99,38 @@ export function BackendSelectionStep() {
           helpText="This becomes the section header [name] in your rclone.conf. Example: azure-prod, backup-s3. Letters, numbers, dashes, underscores only."
         />
         <RemoteNamePreview value={remoteName} />
-        <div data-testid="backend-cards" className="grid grid-cols-1 sm:grid-cols-2 gap-3 mt-4">
-          {Object.entries(BACKEND_REGISTRY).map(([type, entry]) => (
+        <input
+          type="search"
+          value={searchQuery}
+          onChange={(e) => setSearchQuery(e.target.value)}
+          placeholder="Search backends..."
+          className="w-full px-4 py-2.5 rounded-xl border border-outline bg-surface-container text-on-surface placeholder:text-on-surface-variant/50 focus:outline-none focus:ring-2 focus:ring-primary mt-4"
+        />
+        <div data-testid="backend-cards" className="mt-4">
+          {CATEGORY_ORDER.map(cat => {
+            const backends = Object.entries(BACKEND_REGISTRY)
+              .filter(([, e]) => e.category === cat)
+              .filter(([, e]) => !searchQuery || matchesSearch(e, searchQuery));
+            if (backends.length === 0) return null;
+            return (
+              <section key={cat} className="mb-6">
+                <h3 className="text-lg font-semibold text-on-surface mb-3">{CATEGORY_LABELS[cat]}</h3>
+                <div className="grid grid-cols-1 sm:grid-cols-2 gap-3">
+                  {backends.map(([type, entry]) => (
                     <BackendCard
                       key={type}
                       name={entry.displayName}
                       description={entry.description}
                       selected={state.remote.backendType === type}
                       onClick={() => handleCardClick(type as BackendType)}
+                      icon={BACKEND_ICONS[type as BackendType] ? React.createElement(BACKEND_ICONS[type as BackendType]!, { className: 'w-6 h-6' }) : undefined}
                     />
                   ))}
                 </div>
+              </section>
+            );
+          })}
+        </div>
         <div className="flex flex-col sm:flex-row gap-3 mt-6">
           <button type="submit" className={`${MD3_BTN_FILLED} w-full sm:w-auto`}>
             Next