feat(learn): the reference screens as the reworked artifact has them

읽기 연습. Each mode opens with what the round is and a Start button; the
round is timed, and a finished one reports accuracy and time, keeps the
best per mode and says when it was beaten. In sound mode the written
spelling is among the options — reading it as written is the habit the
drill exists to break, so it is the distractor that matters. Answers stay
marked 450ms when right, 900ms when a rule is shown, 1400ms when wrong.
The best rounds sync (trainer.drill), merged mode by mode: the higher
accuracy, then the faster time.

문법. An All chip, a count on every category, 반말 selected first — it is
what manhwa speech is made of — and each row names its category, so the
list still reads under All.

활용 연습. Words come in random order, not the pool's; the running score
comes back after a reload; a wrong answer shows what was typed beside what
it should have been, then the rule. The pool adds the roadmap's own verbs
and adjectives to the deck's. A form lib/conjugation.js cannot build no
longer leaves the Check button stuck.

문장. The artifact's lesson on the ending word and the 서술어 legend, a count
on each level, and every sentence's place in review — as far along as its
least-known chunk, since the chunks are the cards.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

shared/sync-protocol.mjs

@@ -98,7 +98,12 @@ export const decodePk = (pk) => JSON.parse(pk);
  * `server.*` holds this device's endpoint and bearer token, and `sync.*`
  * is this device's own position in the conversation with the server.
  */
-const SYNCABLE_META_EXACT = new Set(["grammar.learned", "grammar.notes", "trainer.conjugation"]);
+const SYNCABLE_META_EXACT = new Set([
+  "grammar.learned",
+  "grammar.notes",
+  "trainer.conjugation",
+  "trainer.drill",
+]);
 const SYNCABLE_META_PREFIX = ["prefs.", "road.", "learner.", "reset."];
 
 export function isSyncableMetaKey(key) {