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/server/index.ts

@@ -32,6 +32,7 @@ export { effectivePromptSegments, allSegmentPaths, readPromptOverride } from "..
 // Importing this module runs the idempotent boot fill-gap — every consumer
 // keeps its plain process.env reads (that seam is the point).
 export * from "./keys.ts";
+export * from "./search.ts";
 export { authStore } from "../store/auth.ts";
 export * from "./settings-body.ts";
 export * from "./turn-liveness.ts";