feat(admin-ui): поиск справочников + счётчик активных записей

Backend:
- DictionaryRecordRepository.countActiveGroupedByDictionary — один GROUP BY
  по всем справочникам с фильтром по scope, без N+1.
- DictionaryResponse.recordCount (nullable) + factory from(d, count).
- DictionaryDefinitionController передаёт счётчики в list/get,
  фильтрованные по currentScopes() пользователя.

Frontend:
- SearchInput над сеткой карточек, client-side filter по
  name/displayName/description (case-insensitive, useDeferredValue).
- Badge "N записей" (i18n plural ru/en) в углу карточки.
- "Показано N из M" рядом с поиском.
- EmptyState когда поиск пустой.

ordinis-admin-ui/src/routes/dictionaries.index.tsx

@@ -1,20 +1,45 @@
-import { useState } from 'react'
+import { useDeferredValue, useMemo, useState } from 'react'
 import { createFileRoute, Link, useNavigate } from '@tanstack/react-router'
 import { useTranslation } from 'react-i18next'
-import { Alert, Badge, Button, EmptyState, LoadingBlock, PageHeader } from '@nstart/ui'
+import {
+  Alert,
+  Badge,
+  Button,
+  EmptyState,
+  LoadingBlock,
+  PageHeader,
+  SearchInput,
+} from '@nstart/ui'
 import { PlusIcon } from '@phosphor-icons/react'
 import { useDictionaries } from '@/api/queries'
+import type { DictionaryDefinition } from '@/api/client'
 import { DictionaryEditorDialog } from '@/components/schema/DictionaryEditorDialog'
 
 export const Route = createFileRoute('/dictionaries/')({
   component: DictionariesPage,
 })
 
+const matchesQuery = (d: DictionaryDefinition, q: string): boolean => {
+  if (!q) return true
+  const haystack = [d.name, d.displayName ?? '', d.description ?? '']
+    .join(' ')
+    .toLowerCase()
+  return haystack.includes(q)
+}
+
 function DictionariesPage() {
   const { t } = useTranslation()
   const navigate = useNavigate()
   const { data, isLoading, error } = useDictionaries()
   const [createOpen, setCreateOpen] = useState(false)
+  const [query, setQuery] = useState('')
+  const deferredQuery = useDeferredValue(query)
+
+  const filtered = useMemo(() => {
+    if (!data) return []
+    const q = deferredQuery.trim().toLowerCase()
+    return data.filter((d) => matchesQuery(d, q))
+  }, [data, deferredQuery])
 
   const createButton = (
     <Button
@@ -69,34 +94,59 @@ function DictionariesPage() {
         actions={createButton}
       />
 
-      <div className="grid grid-cols-1 md:grid-cols-2 lg:grid-cols-3 gap-4">
-        {data.map((d) => (
-          <Link
-            key={d.id}
-            to="/dictionaries/$name"
-            params={{ name: d.name }}
-            className="block bg-white border border-regolith rounded-lg p-4 transition shadow-card hover:shadow-hover hover:border-ultramarain/40"
-          >
-            <div className="flex items-start justify-between mb-2 gap-2">
-              <h2 className="font-primary text-base text-ultramarain">
-                {d.displayName ?? d.name}
-              </h2>
-              <Badge variant="info">{d.scope}</Badge>
-            </div>
-            {d.description && (
-              <p className="text-sm text-carbon line-clamp-2 mb-3">{d.description}</p>
-            )}
-            <div className="flex gap-2 text-2xs uppercase tracking-label text-carbon/60">
-              <span>v{d.schemaVersion}</span>
-              <span>·</span>
-              <span>{d.bundle}</span>
-              <span>·</span>
-              <span>{d.supportedLocales.join(', ')}</span>
-            </div>
-          </Link>
-        ))}
+      <div className="flex flex-col sm:flex-row sm:items-center gap-3">
+        <div className="flex-1 max-w-md">
+          <SearchInput
+            value={query}
+            onChange={(e) => setQuery(e.target.value)}
+            placeholder={t('dict.list.search.placeholder')}
+            aria-label={t('dict.list.search.placeholder')}
+          />
+        </div>
+        <span className="text-sm text-carbon/70">
+          {t('dict.list.found', { shown: filtered.length, total: data.length })}
+        </span>
       </div>
 
+      {filtered.length === 0 ? (
+        <EmptyState title={t('dict.list.search.empty')} />
+      ) : (
+        <div className="grid grid-cols-1 md:grid-cols-2 lg:grid-cols-3 gap-4">
+          {filtered.map((d) => (
+            <Link
+              key={d.id}
+              to="/dictionaries/$name"
+              params={{ name: d.name }}
+              className="block bg-white border border-regolith rounded-lg p-4 transition shadow-card hover:shadow-hover hover:border-ultramarain/40"
+            >
+              <div className="flex items-start justify-between mb-2 gap-2">
+                <h2 className="font-primary text-base text-ultramarain">
+                  {d.displayName ?? d.name}
+                </h2>
+                <Badge variant="info">{d.scope}</Badge>
+              </div>
+              {d.description && (
+                <p className="text-sm text-carbon line-clamp-2 mb-3">{d.description}</p>
+              )}
+              <div className="flex items-center justify-between gap-2 text-2xs uppercase tracking-label text-carbon/60">
+                <div className="flex gap-2 min-w-0">
+                  <span className="truncate">v{d.schemaVersion}</span>
+                  <span>·</span>
+                  <span className="truncate">{d.bundle}</span>
+                  <span>·</span>
+                  <span className="truncate">{d.supportedLocales.join(', ')}</span>
+                </div>
+                {typeof d.recordCount === 'number' && (
+                  <Badge variant="neutral">
+                    {t('dict.list.recordCount', { count: d.recordCount })}
+                  </Badge>
+                )}
+              </div>
+            </Link>
+          ))}
+        </div>
+      )}
+
       <DictionaryEditorDialog
         open={createOpen}
         mode={{ kind: 'create' }}