fix(offline): cold-boot offline from the persisted session + profile

An installed PWA relaunched with the network off hung on the splash: C1's
precache served the shell, but bootstrap() adopted the session and fetched the
profile over the network, which hung. Persist the profile (on every online
adopt + refresh, cleared on logout) and short-circuit bootstrap when the
deliberate offline flag is sticky-on: with a cached session + profile, skip the
network and land straight in the offline lobby. Without a cached profile (never
online), drop the sticky flag and boot online — the first launch must be online.

- session.ts: saveProfile/loadProfile/clearProfile (mirror saveSession).
- offline.ts: shouldBootOffline decision (unit-tested).
- app.svelte.ts: persist in adoptSession + refreshProfile, clear on logout,
  the offline boot short-circuit in bootstrap.

Docs: ARCHITECTURE. Online cold-start unaffected (e2e 196); the offline boot is
contour-verified (the mock e2e cannot enter sticky-offline).

ui/src/lib/app.svelte.ts

@@ -43,6 +43,9 @@ import { parseStartParam } from './deeplink';
 import {
   clearOnboarding,
   clearSession,
+  clearProfile,
+  loadProfile,
+  saveProfile,
   loadOnboarding,
   loadPrefs,
   loadSession,
@@ -53,6 +56,8 @@ import {
 } from './session';
 import type { CoachSeries } from './coachmark';
 import { connection, reportOffline, reportOnline, resetConnection } from './connection.svelte';
+import { offlineMode, setOfflineMode } from './offline.svelte';
+import { shouldBootOffline } from './offline';
 import { isConnectionCode } from './retry';
 import { clearGameCache, getCachedGame, setCachedGame } from './gamecache';
 import { advanceCached } from './gamedelta';
@@ -460,6 +465,7 @@ export async function refreshProfile(): Promise<void> {
   if (!app.session) return;
   try {
     app.profile = await gateway.profileGet();
+    void saveProfile(app.profile); // keep the offline-boot cache fresh
   } catch {
     // Best-effort; the banner just stays as it was until the next fetch.
   }
@@ -517,6 +523,9 @@ async function adoptSession(s: Session): Promise<void> {
   await saveSession(s);
   try {
     app.profile = await gateway.profileGet();
+    // Persist the profile so a later offline cold start can launch from it (its variant
+    // preferences, dictionary versions and display name) without a network fetch.
+    void saveProfile(app.profile);
     // The live interface language follows the device — the explicit local choice (saved in
     // prefs) or the system guess made at bootstrap — and is no longer overridden from the
     // account here: the Telegram bot a user signs in through must not dictate the UI, so a
@@ -790,6 +799,24 @@ export async function bootstrap(): Promise<void> {
   // and skipped in the mock build; see lib/pwa.svelte.
   registerServiceWorker();
 
+  // Deliberate offline mode carried over from a prior session: with no network the session adoption
+  // + profile fetch below would hang the splash, so skip them and launch straight from the cached
+  // session + profile into the offline lobby. Without both (e.g. cleared storage, or an install that
+  // was never online), drop the sticky flag and fall through to the normal online flow — the first
+  // launch must be online.
+  if (offlineMode.active) {
+    const [offlineSession, offlineProfile] = await Promise.all([loadSession(), loadProfile()]);
+    if (shouldBootOffline({ offlineActive: true, hasSession: !!offlineSession, hasProfile: !!offlineProfile })) {
+      gateway.setToken(offlineSession!.token);
+      app.session = offlineSession!;
+      app.profile = offlineProfile!;
+      if (router.route.name === 'login' || router.route.name === 'confirm') navigate('/');
+      app.ready = true;
+      return;
+    }
+    setOfflineMode(false);
+  }
+
   const saved = await loadSession();
   // A VK ID web-link callback (?code&device_id&state) rides the URL after the redirect back
   // from VK; capture and clear it here (it needs the restored session to link against).
@@ -1023,6 +1050,7 @@ export async function logout(): Promise<void> {
   app.splashDone = false;
   gateway.setToken(null);
   await clearSession();
+  await clearProfile();
   app.session = null;
   app.profile = null;
   navigate('/login');