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/composer.tsx

@@ -59,7 +59,7 @@ export function Composer({
 				placeholder="Ask, answer, or steer the lesson…"
 				autoFocus={autoFocus}
 				rows={1}
-				className="field-sizing-content max-h-48 min-h-10 flex-1 resize-none bg-transparent px-2.5 py-2 text-sm outline-none placeholder:text-muted-foreground"
+				className="field-sizing-content font-prose max-h-48 min-h-10 flex-1 resize-none bg-transparent px-2.5 py-2 text-sm outline-none placeholder:text-muted-foreground"
 			/>
 			{verdict && !busy ? (
 				// The plan verdict (docs/probe-teach-split.md §4): accept