Chat mode, phase 2: local history, answer actions, motion polish

- Conversations in a versioned IndexedDB store (freezmo-chat v1, zod
  validated with the same schema backup/sync use, capped at 100 x 300).
  Settled turns persist (question always; answer when produced, partial
  stops included); ?c=<id> keeps reloads on the conversation via
  history.replaceState (no router round-trip mid-chat).
- History UI: desktop column, phone sheet (spring, backdrop, Escape),
  auto titles from the first question, inline rename, delete with an
  Undo toast, diacritic-folding search over titles and message text.
  Scope and model are remembered per conversation; history is readable
  offline.
- Assistant actions: Turn into flashcards (New deck with the answer as
  notes, landing on the options step - deck seed gained step) and Save
  to notes (appends to the single scoped deck, trimmed at 40k).
- Chats travel in the backup export (preview counts them) and in the
  encrypted sync payload; still never the key.
- Motion from lib/motion.ts: message fade-up, sheet springs for the
  model/context/history sheets, 150ms composer height transition, all
  skipped under reduced motion.
- Tests: chat suite 63 -> 89 checks (history, reload, rename/search/
  delete/undo, actions, export, two-device sync round-trip, offline,
  desktop panel). Full set: 12/12 suites, 513 checks. SW -> freezmo-v33.

Also: tests/model-compare.mjs benchmark (diagnostic) for deciding the
default text model on numbers; defaults unchanged.

lib/sync.ts

@@ -13,6 +13,7 @@
 import { z } from "zod";
 
 import { backupDataSchema } from "./backup";
+import { chatHistoryStore, ensureChatsHydrated, replaceChats } from "./chat-store";
 import { ApiError } from "./client-api";
 import { replaceFolders } from "./folders";
 import { replaceHomework } from "./homework";
@@ -162,6 +163,7 @@ async function apiDelete(id: string): Promise<void> {
 
 async function buildPayload(): Promise<SyncPayload> {
   await ensureLearningHydrated();
+  await ensureChatsHydrated();
   return {
     app: "freezmo",
     kind: "sync",
@@ -173,6 +175,7 @@ async function buildPayload(): Promise<SyncPayload> {
       homework: homeworkStore.getSnapshot(),
       history: learningStore.getAnswersSnapshot(),
       srs: learningStore.getSrsSnapshot(),
+      chats: chatHistoryStore.getSnapshot(),
     },
   };
 }
@@ -185,6 +188,7 @@ async function applyRemote(key: CryptoKey, remote: { updatedAt: number; envelope
     replaceFolders(parsed.data.folders);
     replaceDecks(parsed.data.decks);
     replaceHomework(parsed.data.homework);
+    replaceChats(parsed.data.chats ?? []);
   });
   await replaceLearning(parsed.data.history ?? [], parsed.data.srs ?? []);
   setSyncRecord({ lastSyncedAt: remote.updatedAt, dirtyAt: null, conflict: false });