practice polish: no phantom wake, Practice header tag, honest meta

- needsContinuation: a persisted problem-pose ack (terminate:true ended
  the turn deliberately) owes no continuation — reloads after a pose no
  longer wake a phantom turn; error results stay owed like any
  interrupted tool.
- Chat header: practice sessions swap the phase chip for a quiet
  Practice tag (no probe→teach arc applies) and hide the coverage ring
  (practice never extracts — an ever-filling ring would lie).
- ChatSummary gains pendingProblem (activeProblemOf at projection); the
  sidebar meta says 'Problem waiting' for a practice row with a posed
  problem. Kind threads through Chat/[id] page.
- Home picker chip gains Clear (picks were otherwise irremovable).

tests/practice-record.test.ts

@@ -17,6 +17,7 @@ import {
 	concludedByDismissalPair,
 	newProblemDismissedMarker,
 	newThinkingMessage,
+	needsContinuation,
 	newUserMessage,
 	pendingProblemDismissalOf,
 	toLlmMessages,
@@ -262,3 +263,42 @@ describe("toLlmMessages (practice shapes)", () => {
 		assert.equal(out[1]!.role, "toolResult");
 	});
 });
+
+// ── the continuation fold's practice carve-out ──────────────────────────────
+
+describe("needsContinuation (a persisted pose ack owes nothing)", () => {
+	it("a record ending on a problem-pose ack does NOT wake a continuation", () => {
+		// The pose's terminate:true ended that turn deliberately; the
+		// ack persists (unlike a question's placeholder). Without the
+		// carve-out, a reload after a posed problem would wake a
+		// phantom turn (owner design, 2026-10-04).
+		assert.equal(needsContinuation(problemPose()), false);
+	});
+
+	it("a mixed batch (conclude ack then pose ack) still owes nothing — the pose is terminal", () => {
+		const messages = [
+			...problemPose("call_p0", "the earlier one"),
+			concludeCall("solved"),
+			{
+				id: "msg_r_conclude",
+				role: "toolResult",
+				toolCallId: "call_conclude_solved",
+				toolName: PRACTICE_CONCLUDE_TOOL,
+				content: [{ type: "text", text: CONCLUDE_ACK_TEXT }],
+				details: null,
+				isError: false,
+				timestamp: 4,
+			} as LhMessage & ToolResultMessage,
+			...problemPose("call_p2", "the next one"),
+		];
+		assert.equal(needsContinuation(messages), false);
+	});
+
+	it("an ERROR result is not a pose — the agent loop continues past it, so a record ending there (an abort) is owed the wake like any interrupted tool", () => {
+		const messages = [...problemPose("call_pe")];
+		const err = messages[1] as LhMessage & ToolResultMessage;
+		err.isError = true;
+		err.content = [{ type: "text", text: "A problem is already active." }];
+		assert.equal(needsContinuation(messages), true);
+	});
+});

tests/render-sidebar.test.tsx

@@ -27,6 +27,7 @@ function item(overrides: Partial<ChatListItem>): ChatListItem {
 		messageCount: 4,
 		phase: "probe",
 		pendingQuestion: false,
+		pendingProblem: false,
 		busy: false,
 		...overrides,
 	};
@@ -135,4 +136,9 @@ describe("SessionRow practice badge (practice sessions, 2026-10-04)", () => {
 		const html = render(item({ busy: true }));
 		assert.match(html, /Teacher is working…/);
 	});
+
+	it("a practice row with a posed problem says the problem is waiting", () => {
+		const html = render(item({ kind: "practice", pendingProblem: true }));
+		assert.match(html, /Problem waiting ·/);
+	});
 });