feat(search): Tavily + Brave behind a search-provider port; Google CSE retires

Search port + model slots wave, chunk A (owner design, 2026-09-20):
- core/search.ts: SearchHit + SearchProvider port + SearchStatus —
  pure, browser-safe; adapters arrive as injected dependencies.
- server/search.ts: Tavily + Brave adapters (wire shapes VERIFIED
  against docs.tavily.com's OpenAPI + Brave's dashboard docs — Tavily
  auth is the Bearer header, not the legacy body api_key; Brave is
  X-Subscription-Token) + engine resolution per owner decisions: a key
  ALONE activates its engine (no engine choice needed), explicit
  agent.search.engine pins the preference (both keys: Tavily first),
  a pinned engine with a missing key is honestly unavailable — no
  silent fallback, no default engine.
- Curated keys catalog: GOOGLE_SEARCH_API_KEY/GOOGLE_CSE_ID retire
  (CSE closed to new customers, dies Jan 2027 — stored values become
  preserved unknown vars); TAVILY_API_KEY (tvly- shape) + BRAVE_API_KEY
  (length guard) join. UI keys-section TOOL_IDS now derives from the
  catalog — cannot drift.
- GET /api/search: {available, engine, reason} — the honest status for
  the settings gray-out; researcher-disable semantics ride the same
  signal (Teacher stream rewires the tool onto the port).
- agent.search settings field (schema + sanitizer + strict parser);
  web.ts's WebSearchResult is now the core SearchHit (re-exported).

app/api/search/route.ts

@@ -0,0 +1,18 @@
+/**
+ * GET /api/search — the search engines' status (search wave, 2026-09-20):
+ * the honest availability signal the settings UI explains from (the
+ * gray-out affordance) and any client surface can read.
+ *
+ * { available, engine, reason } — never a key, never a secret: `engine` is
+ * the ACTIVE engine when live (auto-detection or the explicit pin), and
+ * `reason` is the one-line state explanation ("set a Tavily or Brave
+ * search API key", or the pinned-engine-key-missing case).
+ */
+
+import { searchStatus } from "@/src/server";
+
+export const dynamic = "force-dynamic";
+
+export async function GET() {
+	return Response.json(searchStatus());
+}