question tools: phase-visible names, hardened teach schemas, context-slim seams

The tools_fails_2 diagnosis (glm-5.3 dropping trailing required fields):
- probe-phase quiz/explain renamed to probe/recall — a shared name carried
  the probe call shape into teaching (the first teach quiz dropped nodeId);
  display seams accept the old names forever
- teach quiz+explain schemas lead with the required pair (type, nodeId);
  explain gains the predict/check type and joins the reveal law (checks
  collapse, predictions arrive open; no-type records render check-style)
- plan_init/probe_done results go context-slim (owner, context diet):
  content = validated nodeIds + binding-id reminder / fixed ack; details
  keeps the tree for the popup and {ok:true} — serializer-verified that
  details never reaches the model; failure echoes dropped
- the cards carry the tool's own name (Probe/Recall) and the quiz type
  reads on the label (Prediction/Check) in composer and transcript

components/answered-card.tsx

@@ -52,7 +52,20 @@ export function AnsweredCard({ answer }: { answer: QuestionAnswerData }) {
 			data-testid="answered-card"
 		>
 			<div className="mb-1 flex items-center gap-2 text-xs font-medium uppercase tracking-wide text-muted-foreground">
-				{isQuiz ? (answer.questionType === "predict" ? "Prediction" : "Quiz") : isExplain ? "Explain" : "Question"}
+				{/* The tool's OWN name first (owner 2026-10-09): probe-phase
+			    cards label Probe/Recall — the phase boundary visible in the
+			    transcript. No `tool` on old records: kind labels as before. */}
+				{answer.tool === "probe"
+					? "Probe"
+					: answer.tool === "recall"
+						? "Recall"
+						: isQuiz
+								? answer.questionType === "predict"
+									? "Prediction"
+									: "Check"
+									: isExplain
+										? "Explain"
+											: "Question"}
 				{isQuiz &&
 					(answer.dontKnow ? (
 						<span className="rounded bg-muted px-1.5 py-0.5">didn't know</span>