dictation feel: finish-first submits, composer focus on run end

Two owner rulings, 2026-10-01 ('nothing gets lost' round):

1. SUBMIT FINISHES DICTATION FIRST. Every submit path — the dock's
   answer (Enter/Cmd+Enter/button) and the composer's send — stops any
   live run and lets Deepgram's last finals land in the target field
   BEFORE building the payload. Dictation.finish() resolves at cleanup,
   post-flush; a module finisher registry (same pattern as the question
   target) hands it to the dock without a prop bridge. Field values are
   read from REF MIRRORS (thinkingTextRef/answerTextRef, the composer's
   textRef): the flush lands via setState after an await, invisible to
   the closure. The quiz flow the owner described now holds: dictate
   reasoning → pick answer → pick confidence → Enter → dictation ends,
   reasoning saved into the thinking field, THEN the answer submits.
   The composer stays sendable while a run is live (its spoken text is
   deferred in the run's buffer) so Enter can trigger the finish-first
   send at all; nothing said → the send no-ops.

2. RUN END FOCUSES THE BARE COMPOSER. The falling edge of
   dictation.active focuses the composer's textarea — only when the
   composer is mounted: a pending question unmounts it (ref null, no
   focus), so the thinking field is deliberately left alone. Composer
   gains an optional inputRef for the page's focus handle.

components/composer.tsx

@@ -31,6 +31,7 @@ export function Composer({
 	onStop,
 	canSend,
 	autoFocus,
+	inputRef,
 	onEscape,
 	placeholder = "Ask, answer, or steer the lesson…",
 }: {
@@ -41,6 +42,9 @@ export function Composer({
 	onStop: () => void;
 	canSend: boolean;
 	autoFocus?: boolean;
+	/** The page's handle to the textarea — the dictation-end focus (owner,
+	 *  2026-10-01): a run ending hands the cursor to the bare composer. */
+	inputRef?: React.RefObject<HTMLTextAreaElement | null>;
 	/** Escape while a dictation runs stops it (STT wave, 2026-09-17). No-op
 	 *  when absent — Esc otherwise means nothing in the composer. */
 	onEscape?: () => void;
@@ -61,6 +65,7 @@ export function Composer({
 			}}
 		>
 			<textarea
+				ref={inputRef}
 				value={value}
 				onChange={(e) => onChange(e.target.value)}
 				onKeyDown={(e) => {