Wave-5 refinement round 2 (owner's batch)

- Home view: StatsBar under the composer (model+thinking control) — the
  DOCK geometry matches the chat view (max-w-[46rem] px-4) so nothing
  shifts when a session starts; pre-chat selection persists via deferred
  save (ModelControl chatId-empty) + PUT after POST /api/chats.
- Answer marks (✓/✗): same visual size as row text, vertically centered;
  colored green-500/red-500 matching the verdict chips.
- All user-typed inputs (composer, question-dock text/thinking/Other,
  answered-card 'your thinking' and free-text records) now render
  Source Sans 3 via the font-prose utility. Placeholders inherit the
  family via the element.
- Answered-card explanation: markdown wrapper made truly inline so the
  'Why:' label + the paragraph sit on one line — removes the oversized
  leading gap.

components/model-picker.tsx

@@ -117,6 +117,13 @@ export function ModelControl({
 	const save = useCallback(
 		async (next: ChatSettings) => {
 			setError(null);
+			// Home view (pre-chat): defer — the selection rides along on the
+			// chat POST and is PUT after creation (onSaved is still lifted).
+			if (!chatId) {
+				onSaved(next);
+				setOpen(null);
+				return;
+			}
 			try {
 				const res = await fetch(`/api/chats/${chatId}/settings`, {
 					method: "PUT",