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/core/contracts/jobs.ts

@@ -68,6 +68,24 @@ export interface UsageStepLike {
 	outputTokenDetails?: { reasoningTokens?: number } | undefined;
 }
 
+/** pi-ai's Usage shape (input/output/cacheRead/cacheWrite/reasoning?) →
+ * UsageStepLike. Structural — no pi import here; the engine band maps at
+ * its boundaries. */
+export function piUsageToStep(usage: {
+	input: number;
+	output: number;
+	cacheRead: number;
+	cacheWrite: number;
+	reasoning?: number;
+}): UsageStepLike {
+	return {
+		inputTokens: usage.input,
+		outputTokens: usage.output,
+		inputTokenDetails: { cacheReadTokens: usage.cacheRead, cacheWriteTokens: usage.cacheWrite },
+		outputTokenDetails: usage.reasoning !== undefined ? { reasoningTokens: usage.reasoning } : undefined,
+	};
+}
+
 /** Fold one model call's usage into the run's running total (pure). A
  * field neither the total nor the step reported stays undefined; once
  * reported, later unreported calls contribute 0. The `steps` counter is