fix(tools): wire the searchAvailable gate + research/pdf in the probe phase

Fix wave (2026-09-20), two owner-approved fixes:

Fix 1 — the searchAvailable gate was dead code on the live wiring path:
createTeacherTools RECEIVED ctx.searchAvailable but dropped it when
building the inner JobToolContext, so jobTools' research gate always took
its ?? true default (jobTools-direct tests passed; the production path
never saw the signal). Threaded through — the gate now reads the live
server signal on the teacher registry too.

Fix 2 — the prober registry gains the research + pdf dispatch tools
(owner ruling, 2026-09-20): these two are phase-omnipresent — the prober
can verify facts or read learner PDFs while assessing. demo/visual stay
teach-phase-only (they need the lesson's plan context). Same gating as
the teacher side: toggle-filtered, research subject to the search gate
(honestly absent when no engine is live — the prober's dispatch closes
over the SAME jobTools builder, one gate, one semantics). probe_done
stays always-on-by-construction; the learner-fs set untouched.

- ProberToolContext (extends ProbeDoneContext with the job wiring);
  createProberAgent takes it; chat-handler injects jobStore + spawn +
  searchAvailable into the prober ctx.
- TeacherToolContext.spawn's stale input union fixed (PdfInput was
  missing from the TYPE — runtime already passed it).
- Tests: the threaded-gate describe in web-search.test.ts pins the LIVE
  factory path both ways (teacher + prober); question-tools' registry
  key-sets gain research/pdf; the prober toggle test pins the
  research:false path.

Gates: typecheck, 807/807 tests, lint, build — all green.

tests/tool-toggles-bridge.test.ts

@@ -14,7 +14,8 @@ import assert from "node:assert/strict";
 import { z } from "zod";
 import { describe, it } from "node:test";
 import { createProberAgent, createTeacherAgent } from "../src/agent/teacher-agent.ts";
-import type { ProbeDoneContext } from "../src/agent/tools.ts";
+import type { ProberToolContext } from "../src/agent/tools.ts";
+import { jobStore } from "../src/store/jobs.ts";
 import { parseAgentSettingsBody } from "../src/server/settings-body.ts";
 import { chatStore } from "../src/store/chats.ts";
 import type { AgentSettings } from "../src/core/settings.ts";
@@ -32,7 +33,7 @@ describe("AgentBuildOptions.toolToggles (the P2 bridge)", () => {
 
 	it("flows into the prober's registry; probe_done survives everything", () => {
 		const chatId = chatStore.createChat("Toggle bridge test").id;
-		const ctx: ProbeDoneContext = { chatId, chatStore, deliver: () => {} };
+		const ctx: ProberToolContext = { chatId, chatStore, deliver: () => {}, jobStore, spawn: () => {} };
 		const prober = createProberAgent(ctx, { toolToggles: { ask_user_question: false } });
 		const names = toolNames(prober);
 		assert.ok(!names.includes("ask_user_question"), "the delta dropped the tool");