fix: budget dock height for answer controls and toolbar

components/chat.tsx

@@ -2026,11 +2026,23 @@ function DockOverlay({
 		if (!el) return;
 		const measure = () => {
 			setSbInset(Math.round((el.offsetWidth - el.clientWidth) / 2));
-			setDockMaxH(Math.max(el.clientHeight - 32, 160));
+			const block = blockRef.current;
+			const question = block?.querySelector<HTMLElement>("[data-dock-scroll-area]");
+			// The height budget belongs to the whole dock, including answer
+			// controls, stats, and padding. Only the question may consume the
+			// remaining space; otherwise the overlay grows behind the header.
+			const chrome = block && question ? block.offsetHeight - question.offsetHeight : 0;
+			setDockMaxH(Math.max(el.clientHeight - 32 - chrome, 0));
 		};
 		measure();
+		const observer = new ResizeObserver(measure);
+		observer.observe(el);
+		if (blockRef.current) observer.observe(blockRef.current);
 		window.addEventListener("resize", measure);
-		return () => window.removeEventListener("resize", measure);
+		return () => {
+			observer.disconnect();
+			window.removeEventListener("resize", measure);
+		};
 	}, [scrollRef]);
 
 	// GROWTH MUTE (owner round, 2026-10-05 — the generation churn): during a

components/practice-dock.tsx

@@ -105,7 +105,7 @@ export function PracticeDock({ problemCallId, input, expanded, onExpand, onSubmi
 			    cards' label row — owner round, 2026-10-05) + the statement,
 			    markdown + LaTeX rendered, capped by the measured column
 			    (--dock-max-h; the old fixed 40vh cut long problems short). */}
-			<div className="max-h-[var(--dock-max-h,40vh)] overflow-y-auto px-4 pt-3 pb-2">
+			<div data-dock-scroll-area="" className="max-h-[var(--dock-max-h,40vh)] overflow-y-auto px-4 pt-3 pb-2">
 				<div className="mb-1 text-xs font-medium uppercase tracking-wide text-muted-foreground">Problem</div>
 				<div className="lh-prose text-[15px]">
 					<ToolContentResponse>{input.statement}</ToolContentResponse>

components/question-dock.tsx

@@ -564,7 +564,7 @@ function QuestionDockForm({
 			{/* Question area — scrolls internally if very tall; the bottom row stays put.
 			    Capped by the measured column (--dock-max-h; the old fixed 55dvh cut
 			    long questions short — owner round, 2026-10-05). */}
-			<div data-session-find-root="" className="max-h-[var(--dock-max-h,55dvh)] overflow-y-auto px-4 pt-3">
+			<div data-dock-scroll-area="" data-session-find-root="" className="max-h-[var(--dock-max-h,55dvh)] overflow-y-auto px-4 pt-3">
 				<div className="mb-1 text-xs font-medium uppercase tracking-wide text-muted-foreground">
 					{toolName === "probe"
 						? "Probe"