feat(search): web_search onto the injected port — Google CSE retired, research honestly disabled

Chunk A of the search port wave (2026-09-20), per master's assignment:

- web.ts: the Google Custom Search backend is gone — web_search now runs
  on the core search port (SearchProvider), injected as a dependency
  (import law: the tool never imports server code). createWebTools(search)
  resolves the LIVE provider fresh per call; null = the honest
  unavailability string (no silent fallback, owner decision). web_fetch
  unchanged (needs no engine).
- runner: JobRunnerDeps.searchProvider — the server composition threaded
  into the researcher; jobs already in flight when a key disappears still
  fail honestly through the same seam, never crash.
- jobTools: the research dispatch tool DROPS from the teacher's registry
  when ctx.searchAvailable() is false (owner decision: registry-level
  drop — the model never sees the tool, no doomed dispatch, no error
  card). Absent seam = available (tests). chat-handler injects
  server/searchAvailable + searchProvider.
- tests: stubFetch (the Google wire stub) retired; jobs.test.ts threads
  a recording stub provider through all four research runners and asserts
  the scripted query hit the port; new web-search.test.ts covers the
  factory contract (null → honest string, hits, error strings, fresh
  resolution, web_fetch independence) + the registry drop matrix.

Gates: typecheck, 793/793 tests, lint, build — all green.

src/agent/tools.ts

@@ -154,6 +154,10 @@ export interface TeacherToolContext extends PlanToolContext {
 	 *  rides along — the spawn fires mid-stream, before the tool part is
 	 *  persisted to the transcript (a transcript scan would race it). */
 	spawn: (job: JobRecord, input: ResearchInput | DemoInput | VisualInput) => void;
+	/** Search availability (search port wave, 2026-09-20): the research
+	 *  dispatch tool's honest-disable signal — no live engine = the tool
+	 *  drops from this registry (JobToolContext.searchAvailable). */
+	searchAvailable?: () => boolean;
 }
 
 /**