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/core/settings-resolution.ts

@@ -24,6 +24,7 @@
 
 import type { ThinkingLevel } from "@earendil-works/pi-agent-core";
 import type { ChatSettings } from "./contracts/chat.ts";
+import type { SearchEngineId } from "./search.ts";
 import {
 	BACKGROUND_MODEL_ROLES,
 	FACTORY_SETTINGS,
@@ -62,6 +63,10 @@ export interface EffectiveSettings {
 		tools: Record<string, boolean>;
 		/** Delta map as stored — absent key → override off. */
 		prompts: Record<string, boolean>;
+		/** The search-engine preference as stored (search wave, 2026-09-20):
+		 *  passthrough delta — engine resolution (pin → auto → unavailable)
+		 *  lives in server/search.ts, where keys are visible. */
+		search: { engine?: SearchEngineId };
 	};
 	appearance: EffectiveAppearance;
 	graph: Required<GraphSettings>;
@@ -105,6 +110,7 @@ export function resolveSettings(record: UserSettings | null, factory: ModelRoleS
 			models,
 			tools: agent.tools ?? {},
 			prompts: agent.prompts ?? {},
+			search: agent.search ?? {},
 		},
 		appearance: {
 			mode: appearance.mode ?? factoryAppearance.mode,