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).

src/agent/tools/web.ts

@@ -1,5 +1,10 @@
 import { z } from "zod";
 import { lhTool } from "../lh-tool.ts";
+// The search-hit shape lives in the core port since the search wave
+// (2026-09-20) — this module keeps the historical alias so callers don't
+// churn; the tool's rewiring onto the port is the Teacher stream's.
+import type { SearchHit as WebSearchResult } from "../../core/search.ts";
+export type { WebSearchResult };
 import { Readability } from "@mozilla/readability";
 import { parseHTML } from "linkedom";
 import TurndownService from "turndown";
@@ -22,12 +27,7 @@ import TurndownService from "turndown";
  */
 
 // ── web_search ───────────────────────────────────────────────────────────────
-
-export interface WebSearchResult {
-	title: string;
-	url: string;
-	snippet: string;
-}
+// (WebSearchResult is the core SearchHit, re-exported above.)
 
 function searchCredentials(): { apiKey: string; cseId: string } | null {
 	const apiKey = process.env.GOOGLE_SEARCH_API_KEY;