assistant: teach the agent about Search admin

Bring the LLM agent's prompts and tools current with the new /search
section and arcadia-search admin sidecar:

- New tools in admin-tools.ts:
  - list_search_corpora: enumerate tenants + corpora with build status,
    so the agent can pick a real corpus instead of guessing.
  - rebuild_search_corpus(tenant, corpus): isWrite=true, surfaces a
    confirm card. Use after uploads or when results look stale.
- search_kb description updated: names docs / operator-tools / files
  explicitly, and points at list_search_corpora when unsure.
- ARCADIA_KNOWLEDGE: adds search-corpus terminology, /search route,
  and a one-liner pointer to the three new tools.
- assistant.tsx UI_CONTROL_PREFACE: nav-search added, full Search
  page action catalog (search-refresh / -restart / -new-tenant /
  -new-corpus, corpora-search, per-row corpus-{t}-{c}-{rebuild,edit,
  delete,actions}, tenant-{id}-delete, dialog form fields). Recipe
  for the manual rebuild path, plus a note steering the agent to
  the rebuild_search_corpus tool by default.
- search.tsx publishes a "search" surface to admin-context with
  tenants + corpora summary, so the agent gets live state without
  needing a tool call when /search is mounted.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

app/routes/search.tsx

@@ -60,6 +60,7 @@ import {
 } from "~/lib/search-admin"
 import { pageTitle } from "~/lib/page-meta"
 import { useSession } from "~/lib/session"
+import { useRegisterAdminContext } from "~/lib/admin-context"
 
 export const meta = () => pageTitle("Search")
 
@@ -140,6 +141,24 @@ export default function SearchRoute() {
     return { indexed, docs }
   }, [corpora])
 
+  // Publish a snapshot to the assistant's admin context so the agent
+  // can answer "what corpora exist?" / "is the docs corpus indexed?"
+  // without having to call list_search_corpora.
+  const adminSurface = useMemo(
+    () => ({
+      endpoint: searchAdmin.baseUrl,
+      tenants: tenants.map((t) => ({ id: t.id, corpus_count: t.corpus_count })),
+      corpora: corpora.map((c) => ({
+        tenant: c.tenant,
+        corpus: c.corpus,
+        indexed: c.indexed,
+        num_docs: c.num_docs,
+      })),
+    }),
+    [tenants, corpora],
+  )
+  useRegisterAdminContext("search", adminSurface)
+
   const rebuild = useCallback(
     async (tenant: string, corpus: string) => {
       const id = `${tenant}/${corpus}`