Swap the server engine to pi-ai/pi-agent-core (Band B+C of docs/pi-engine-swap.md)

The Vercel AI SDK survives only as Band D (useChat client + UIMessage
record types); @openrouter/ai-sdk-provider is uninstalled.

- src/agent/models.ts: PiEngine {model, streamFn} via createModels +
  openrouterProvider subpath; thinkingLevelFor maps config effort none->off
- src/agent/lh-tool.ts: neutral LhTool (zod authoring, optional execute,
  clientQuestion flag); toPiTool converts via z.toJSONSchema and re-runs
  zod inside execute so refinements ride the error-result retry path
- src/server/pi/record-adapter.ts: UIMessage records -> pi Messages
  (dangling tool calls get synthesized interrupted results)
- src/server/pi/ui-stream.ts: SSE bridge emitting AI-SDK-shaped chunks so
  the useChat client parses unchanged (continuation id rule, question
  tools never emit output, tool-input-error for bad authoring)
- teacher-agent.ts: stateless per-turn pi Agents; shouldStopAfterTurn
  stops only when every question-tool call resolved cleanly (errors retry)
- chat-handler.ts: buildAgent(outgoing) factory seam (stateless doctrine);
  assertValidUiMessages owns the retired SDK validation gate
- sub-agents via shared runSubagent (pi-run.ts); extraction stages stop
  after a clean submit; visual-maker keeps its hand-rolled loop over
  direct streamSimple calls; aborted model calls bill no usage
- tests: all model seams ported to pi-ai faux provider (scripted
  FauxResponseSteps, agent factories); handleChatRequest second param
  is now an agent factory

Gates: tsc, lint, build, 305/305. Live GLM smoke (disposable driver,
deleted): prober streaming + persistence, question seam, turn-2
continuation same message id, per-turn real token usage - ALL PASS.
Data wiped at the pivot (chats/graph/jobs, .gitkeeps kept).

src/agent/tools/jobs.ts

@@ -1,5 +1,5 @@
-import { tool, type ToolSet } from "ai";
 import { z } from "zod";
+import { lhTool, type LhTool } from "../lh-tool.ts";
 import type { JobRecord } from "../../core/contracts.ts";
 import type { JobStore } from "../../core/ports.ts";
 
@@ -103,21 +103,24 @@ const VISUAL_DESCRIPTION =
  * context (chatId + jobStore + the spawn seam), so concurrent chats never
  * share state. chat-handler wires it each turn; tests wire their own.
  */
-export function jobTools(ctx: JobToolContext): ToolSet {
+export function jobTools(ctx: JobToolContext): Record<string, LhTool<any, any>> {
 	return {
-		research: tool({
+		research: lhTool({
+			name: "research",
 			description: RESEARCH_DESCRIPTION,
-			inputSchema: researchInputSchema,
+			schema: researchInputSchema,
 			execute: async (input, { toolCallId }) => dispatch(ctx, "research", toolCallId, RESEARCH_ACK, input),
 		}),
-		demo: tool({
+		demo: lhTool({
+			name: "demo",
 			description: DEMO_DESCRIPTION,
-			inputSchema: demoInputSchema,
+			schema: demoInputSchema,
 			execute: async (input, { toolCallId }) => dispatch(ctx, "demo", toolCallId, DEMO_ACK, input),
 		}),
-		visual: tool({
+		visual: lhTool({
+			name: "visual",
 			description: VISUAL_DESCRIPTION,
-			inputSchema: visualInputSchema,
+			schema: visualInputSchema,
 			execute: async (input, { toolCallId }) => dispatch(ctx, "visual", toolCallId, VISUAL_ACK, input),
 		}),
 	};